Boris Johnson has said "there is a way" of getting a new Brexit deal, as he defended the decision to suspend Parliament for five weeks.
The PM said "loads of people" wanted an agreement, but he was prepared to leave without one if "absolutely necessary".
Parliament will not resume sitting until 14 October, three days before a crucial Brexit summit of EU leaders.
The PM, who has met the leadership of Northern Ireland's DUP, said claims this was undemocratic were "nonsense".
Amid unprecedented scenes in the Commons early on Tuesday, some MPs protested against the suspension with signs saying "silenced" while shouting: "Shame on you."
But Mr Johnson rejected claims this was an affront to democracy, saying the opposition parties were given the chance of an election before the Brexit deadline on 31 October but had spurned it.
Opposition MPs said a law blocking a no-deal Brexit must be implemented before there could be any election.
Labour leader Jeremy Corbyn has promised a further referendum on Brexit with a "credible Leave option" versus Remain if he wins the next general election - but the party is unlikely to commit to either option in its manifesto.
Key sticking point
The prime minister held an hour of talks with Democratic Unionist leader Arlene Foster and her deputy Nigel Dodds in Downing Street.
Mrs Foster, whose party has propped up the Conservative government since the 2017 election, issued a statement later indicating it would not support any revised version of Theresa May's Brexit agreement which separated Northern Ireland from the rest of the UK.
She said renewed talk of a so-called Northern Ireland-only backstop, which would see it remain in the customs union and be bound by EU rules for goods and animal products while the rest of the UK was not, would be "unacceptable".
"A sensible deal, between the United Kingdom and European Union which respects the economic and constitutional integrity of the United Kingdom, is the best way forward for everyone," she said.
"History teaches us that any deal relating to Northern Ireland which cannot command cross community support is doomed to failure. That is why the Northern Ireland backstop is flawed.
"During today's meeting, the prime minister confirmed his rejection of the Northern Ireland only backstop and his commitment to securing a deal which works for the entire United Kingdom as well as our neighbours in the Republic of Ireland."
The Irish border has proved a key sticking point in attempts to agree a Brexit deal between the UK and the EU.
The government has indicated it could support harmonised rules for the agriculture and food sector to prevent the need for any sanitary and other health checks on the border between Northern Ireland and the Republic.
But it has distanced itself from reports that plans for a single EU-UK customs territory in the current withdrawal agreement - rejected three times by MPs - could be replaced with a specific Northern Ireland only "backstop" arrangement.
Although official negotiations with the EU have yet to restart, the bloc's new trade commissioner said it was positive the UK seemed prepared to "accept some level of divergence between Northern Ireland and the rest of the UK".
"I remain hopeful that the penny is finally dropping with the UK that there are pragmatic and practical solutions that can actually be introduced into the debate at this stage - albeit at the 11th hour - that may find some common ground between the EU and the UK," Ireland's Phil Hogan told the Irish Times
Parliament was suspended - or prorogued - at just before 02:00 BST on Tuesday amid noisy protests from opposition MPs.
During the five-week suspension, parties will hold their annual conferences but no debates, votes or committee scrutiny sessions will take place.
Boris Johnson will not face Prime Minister's Questions until the period is over and his scheduled questioning by the Commons Liaison Committee on Wednesday has been cancelled.
Sarah Wollaston, the Lib Dem chair of the committee, said the PM had gone back on earlier "reassurances" that he would appear, telling BBC's Newsnight she was "appalled" that he was "running away from scrutiny".
Parliament's suspension means MPs will not get a third chance to vote for an early election until they return, meaning a poll would not be possible until November at the earliest.
In Monday's latest vote, 293 MPs backed the prime minister's motion for an early election, far short of the two thirds needed.
The Welsh members also gave us a beautiful song. With harmony! 🏴 pic.twitter.com/iXV8xeuDoX— Hannah Bardell 🏴🏳️🌈 (@HannahB4LiviMP) September 10, 2019
New legislation, which was granted royal assent on Monday, will force the prime minister to seek a delay until 31 January 2020 unless a deal - or a no-deal exit - is approved by MPs by 19 October.
Speaking during a visit to a primary school in London, Mr Johnson said getting ready to leave the EU on Halloween was among the "priorities of the people".
He said there "were loads of people around the place", including in Brussels, who wanted to nail down an agreement but he was willing to leave without a deal "if absolutely necessary".
"There is a way of getting a deal but it will take a lot of hard work - but we must be prepared to come out without a deal."
Labour, the SNP, the Liberal Democrats, the Green Party, the Independent Group for Change and Plaid Cymru have refused to agree to an election on what they say are "Boris Johnson's terms".
Speaking at the TUC Congress on Tuesday, Mr Corbyn said "our priority is to stop no deal - and then have a general election".
The Lib Dems, meanwhile, are seeking to put distance between themselves and Labour by saying that if they win power at the next election they will have an "unequivocal" mandate to cancel Brexit entirely.
At their conference on Sunday, members will debate a motion reaffirming their support for a referendum, but also urging the revocation of Article 50 - the legal process for leaving the EU - a week before the Brexit deadline if no deal has been agreed.
The prime minister's self-imposed Halloween Brexit deadline looks further out of reach than a few short days ago.
Is it impossible? Absolutely not.
There is the possibility, still, of a deal, with Number 10 today stressing it is still their primary aim.
Whispers again about a Northern Ireland-only backstop, and a bigger role for the Stormont assembly, if it ever gets up and running, are doing the rounds.
Some MPs and some diplomats are more cheerful about the possibilities of it working out.
If you squint, you can see the chance of an agreement being wrapped up at pace, although it seems the chances range somewhere between slim and negligible.