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The prime minister has released a statement after meeting Northern Ireland's main parties saying agreement can be reached to restore a power-sharing executive at Stormont "if there is good will on all sides".
"But time is running short and the parties must come together by the 29 June for the return of a strong voice at Stormont and for a brighter future for everyone in Northern Ireland."
She said Northern Ireland Secretary James Brokenshire would keep talking to the parties "and if no resolution is reached then we will need to consider what steps we need to take, to ensure Northern Ireland has the political stability it needs".
Devolved government in Northern Ireland broke down in January.
BBC political editor Laura Kuenssberg said the Grenfell Tower disaster was an emergency of such gravity that it had already become a significant issue for the government, at a very volatile time.
The priority was to focus on getting help to where it was needed - with the announcement that a scheme to provide extra cash for the council - before getting on with a full public inquiry, which would get going "pretty soon".
But the handling of such an awful situation was very risky for politicians and uncomfortable truths could emerge from the public inquiry.
"Potentially, some people expect, it may well show that not just this government but previous governments have simply not done enough to make sure this kind of housing is safe," she said.
The Grenfell Tower block disaster has again been dominating the news agenda. Here's a round-up of the latest developments on this and other political stories today:
The Lib Dems have warned the Conservatives they "cannot go from weak and wobbly to business as usual" after the government announced formal Brexit negotiations will begin on Monday.
Lib Dem MP Alistair Carmichael said:
If the government cannot even secure a deal with the DUP, how on earth can they get a deal with the EU? Theresa May must immediately create a cross-party joint cabinet committee to negotiate Brexit. It is the only way to unite the country and strengthen our bargaining power with the EU.”
Sinn Fein's Gerry Adams says his party will oppose any pact between the UK government and the DUP "that undermines the Good Friday Agreement".
He said all parties in Northern Ireland "need to be consulted on all of this".
"A little side bargain to keep Theresa May in power - a temporary little arrangement - won't have any integrity and certainly isn't as important as the needs of the people who live in Ireland and particularly in the north of Ireland," he said.
BBC News NI Political Editor
The DUP Deputy Leader Nigel Dodds says the setting of a date for the Queen's Speech is separate and not relevant to his party's discussions over a deal with the Conservatives.
Questioned about whether a deal would be announced before the Queen's speech next Wednesday, Mr Dodds said there's no deadline for the discussions.
Mr Dodds reiterated that the DUP wants to strengthen the UK, deliver Brexit in a proper and sensible manner for Northern Ireland and spread prosperity around the UK.
Asked if the Treasury was "nitpicking" over the financial details, Mr Dodds said he'd seen the reports in the newspapers but wouldn't comment on speculation.
More on the Brexit talks. Formal negotiations will begin on Monday, the UK and EU say.
The announcement by Brexit Secretary David Davis and EU negotiator Michel Barnier follows preliminary talks in Brussels between officials.
The formal negotiations were already due to start on Monday but doubt was cast by the general election result and ongoing talks between the Conservatives and the Democratic Unionists.
The UK is due to leave by the end of March 2019.
Labour MP Harriet Harman has been speaking to the BBC after the Westminster Hall session earlier.
The former party deputy leader is an MP in the London borough of Southwark, where the 2009 Lakanal House fire killed six people.
She said tower blocks needed to be fitted with sprinklers and questions needed to be asked about whether refurbishing blocks could compromise fire safety - and whether the official "stay put" advice for people in burning buildings should be changed.
Of the public inquiry, she said:
There doesn't have to be a delay. It's wrong if there is a delay because people are living in thousands of tower blocks all around the country and they need to know the lessons are going to be learned quickly."
She also said it was up to opposition parties to make sure the government "doesn't slip off the hook" in terms of providing resources to make sure buildings are safe.
Home Secretary Amber Rudd has urged people "not to rush to judgement" over the Grenfell Tower disaster.
Hailing the UK for having "some of the most rigorous fire safety regulations in the world", she stressed: "We need to establish how such a tragedy could have occurred in a major capital in the early 21st century."
Writing in the Evening Standard, she said: "Of course we need to know more about how this tragedy could have happened and there will be a full investigation.
"But at this early stage, with firefighters still picking their way through the debris, I would urge everyone not to rush to judgement. If there are lessons to be learned we will learn them."
She praised the bravery of the emergency services and conceded "these are challenging times" for Londoners, with "heartbreaking images of suffering" filling TV screens.
"My heart goes out to every person affected by this tragedy..." she said.
"We have to dig deep inside ourselves in order to keep going. But even in its darkest days, the spirit of London prevails."
Expressing her "deepest condolences" to those suffering "unimaginable grief", she writes that "history has shown us how strong London is".
"The shadow of this tragedy will stay with us forever — we will stay strong for everyone affected and not be afraid to ask vital questions to ensure this can never happen again."
The House of Commons library has just published a briefing note on fire safety in high-rise acommodation.
It explains the role of building regulations and the government's response to calls for these to be reviewed after another fatal fire, in south-east London in 2009.
Tim Farron was right to resign as Liberal Democrat leader because of his "fundamentally illiberal and prejudiced views" on gay sex, former Lib Dem minister David Laws has said.
Mr Farron announced he was standing down as leader on Wednesday, saying he had been unable to reconcile his Christian faith with the demands of leading a "progressive, liberal" party.
But Mr Laws, who is openly gay, accused the Lib Dem leader of fostering a "dangerous myth" about how people in same-sex relationships should be treated by society.
He said Mr Farron's views had harmed the Lib Dem election campaign, which saw the party gain just four seats rather than making the hoped-for breakthrough.
Writing for the i newspaper, the former chief secretary to the Treasury said:
You cannot be a leader of a liberal party while holding fundamentally illiberal and prejudiced views which fail to respect our party's great traditions of promoting equality for all our citizens."
Mr Laws said "many of us have despaired" that all the "good work" of Liberal Democrats such as Lynne Featherstone, who drove through the equal marriage legislation under the coalition, had been "undermined by Tim's failure to be able to give direct and liberal responses on his own attitudes to homosexuality".
A Liberal Democrat election campaign which should have appealed to liberal voters of all ages has been undermined by the outdated opinions and views which Tim clearly holds."
Former Lib Dem business secretary Sir Vince Cable has urged the chancellor to "hold his ground and put membership of the single market and customs union back on the table".
Sir Vince was reacting to the news that Mr Hammond had cancelled his Mansion House speech in the wake of the Grenfell Tower disaster.
The Lib Dems had hoped the chancellor was going to set out a more pragmatic approach to Brexit that was focused on protecting jobs and the economy.
Sir Vince accused the Conservatives of being "egged on by the DUP" to plough ahead with "a deeply damaging exit" from the single market and customs union.
"The chancellor should hold his ground and put membership of the single market and customs union back on the table. Brexit should be negotiated involving other parties, not by a government in hock to the DUP."
Housing Minister Alok Sharma winds up the Westminster Hall debate on the Grenfell Tower tragedy by saying that "every single family" affected "will be rehoused in the local area" - Labour MPs had been pushing for an early commitment to help reassure those who have lost their homes in the disaster.
Fire Minister Nick Hurd says he understands the need for reassurance for people and says the challenge of rehousing people will be "on the agenda this afternoon" and he hopes to be in a position to make "clearer assurances" afterwards.
On the public inquiry, he says there will be "no stone [left] unturned" because he said ministers "completely understand" the shock, anger, frustration and fear felt in the wake of the Grenfell Tower tragedy.
He says it was a "very unusual fire" that had yet to be fully understood. It should not happen in Britain, he says, but it appeared to have been an unusual fire in terms of its scale and the speed at which it spread.
The government had to proceed "on a basis of strong evidence and fact", he said.
Minister Nick Hurd describes events as a "national tragedy" as MPs wrap up their discussion of events in Westminster Hall. He says the discussion had reflected the "deep profound shock" that was felt across the country by the disaster.
"If you've stood at the bottom of that building and looked up, nothing you can see on the TV can prepare you" he says for the "terror that must have been felt" on that night. He praises the bravery of firefighters who went in.
"That shock and sadness have been very well articulated today," he says, adding anger in the community was "understandable" and must be listened to by the government, the minister says.
Labour leader Jeremy Corbyn says all the questions that have been asked are serious and require answers.
He calls on ministers to give an assurance that there will be a written statement about how they are dealing with this inquiry and asks them to provide a full statement on this whole process.
He argues that "it's simply not satisfactory that we're meeting in Westminster Hall" when MPs have raised very important issues that need answers.
He adds that the public also need "reassurance" and above all those that have lost their homes need to know they have somewhere to stay "permanently in the community they love".
House of Commons
Labour's Kate Green says residents need to know what to do in the face of a tower block blaze.
She says it will be "very difficult to persuade frightened people" now that the best advice is to stay in their property, in the wake of the Grenfell Tower blaze.
"Everything we know about fire deaths and this kind of atrocity is its the poorest people in the poorest properties that are the most vulnerable," she says.
Labour MP for Brighton Kempton Lloyd Russell-Moyle says people in tower blocks have been contacting him to say they now cannot sleep they are so worried about the potential for fire.
The fire service must have full resources to do full inspections across all blocks within a week, he says "so that residents can sleep easy at night", as they have lost faith in other bodies, he says.
Downing Street has confirmed that the public inquiry into the Grenfell Tower tragedy will be led by a judge.
In Westminster Hall, Richmond Park MP Zac Goldsmith said he has had emails from people in tower blocks across London who were "desperately anxious" about their own accommodation.
He says local authorities must be "charged with that responsibility" - for reviewing accommodation - as a matter of urgency and must get resources to do so, within days or weeks "not months".
In Westminster Hall, Conservative MP James Cleverly, a former chairman of the London Fire and Emergency Planning Authority, says this will be the "most significant and harrowing event" that many firefighters will have had to deal with an an "enhanced support package" was also needed for them - as well as for residents.
Labour's Seema Malhotra, MP for Feltham and Heston, says the west London coroners' service face much "strain and stress" which must be matched with extra resources.
The proceedings in the Grand Committee Room are not following the pattern of a statement in the Commons chamber, with two ministers responding to questions.
Labour leader Jeremy Corbyn, who spoke earlier, is among the MPs listening.
Conservative Vicky Ford says: "There will be many people who work in tall buildings .. and they too will be fearful."
Any findings into stopping such fires in residential buildings should also cover workplaces, she says.
Home Office Minister Nick Hurd said he wanted to reassure MPs that the government would do "everything that we can" to support Kensington and Chelsea in providing those who have lost their homes with suitable housing.
Karen Buck, Labour MP for Westminster North, said it should be possible to go to the housing associations and private providers in London today and make a commitment that every family and household will be guaranteed accommodation locally. That is needed to reduce "fear and anxiety", she said.
Mr Hurd says the point is "well made" and he will take it to the next cross-government meeting he is attending.
Housing minister Alok Sharma said the government "stands ready to provide any assistance necessary" to the emergency services and local authority.
"We will support every family who is affected," he told MPs.
Work was under way to carry out checks on other buildings, he said.
"We do recognise that we need to be taking action .. to get the answers that everybody wants," he said.
In Westminster Hall, Labour Leader Jeremy Corbyn has said he "feels very angry" about the way the fire spread and how the community has been left "traumatised".
Residents he met were angry that they had raised concerns about safety and had not received any answers. Everybody living in a tower block will now be frightened, Mr Corbyn said.
The public inquiry must be swift, he said, and he suggested empty luxury flats in the area should "requisitioned" to prevent the victims being farmed out to seaside "bed and breakfasts".
Labour MP David Lammy has made a plea for criminal investigations to be launched in the aftermath of the Grenfell Tower fire, during a specially arranged session in Westminster Hall.
He spoke about a friend who lived on the 20th floor of the block and who is still missing. He said she had posted on Facebook at 3 o'clock to say she was "feeling faint".
The grand committee room is packed with MPs and the media as London Labour MPs are lining up to call for action and accountability.
Karen Buck said "we cannot wait years" to make safety improvements.
She said the government must provide cash to make sure no-one is made homeless by the tragedy and for legal assistance.
More from Westminster Hall where Fire Minister Nick Hurd is taking questions about the Grenfell Tower tragedy from MPs.
New Labour MP for Kensington Emma Dent Coad said the community had been "traumatised" and said it must be a priority to ensure survivors remained together when they were re-housed.
She called for an "urgent, transparent and detailed response" adding: "They need answers."
Labour's John Healey said the PM did not have to wait for the outcome of public inquiry to take action and should start installing sprinklers in high-rise blocks across the country and should implement the findings of inquest into a previous fire.
Mr Hurd, a Conservative, said: "Our focus remains on the immediate emergency response and ensuring we are supporting people affected by this tragedy."