The prime minister has confirmed the general election will take place as planned on 8 June, despite another terrorist attack in London.
Speaking outside Downing Street, she said: "Violence can never be allowed to disrupt the democratic process."
Political campaigning would resume in full on Monday, she said, after most parties suspended national campaigns.
Seven people were killed in the attack near London Bridge, the third terrorist attack in the UK in three months.
UKIP is the only major party to say it would not suspend national campaigning on Sunday, just days before the vote, with leader Paul Nuttall arguing that was "what the extremists would want".
The terrorist attack began when a white van hit pedestrians on London Bridge at 21.58 BST on Saturday, before three men got out and stabbed people in nearby Borough Market.
Seven people have been killed and scores injured. The three attackers were shot dead by police.
The prime minister gave a statement after chairing a meeting of senior ministers and security chiefs in the government's emergency Cobra committee on Sunday morning.
Mrs May said: "As a mark of respect the two political parties have suspended our national campaigns for today.
"But violence can never be allowed to disrupt the democratic process, so those campaigns will resume in full tomorrow and the general election will go ahead as planned on Thursday."
The prime minister said the country must "pull together" and unite to "defeat our enemies" and said "things need to change" in the way that extremism and terrorism are tackled.
Shadow Foreign Secretary Emily Thornberry criticised the prime minister for her statement, telling BBC Radio 4's The World This Weekend: "I don't think it's right to get dragged into plans at this stage so soon after those attacks."
Asked if the announcement strayed into party politics, she said: "I think that it is drawing us into a debate. I think that there is time enough for us to discuss these issues."
She added: "I just simply regret the approach that she [Mrs May] has taken."
Labour Leader Jeremy Corbyn said he was "absolutely shocked and horrified" at the attack, but added: "If we allow these attacks to disrupt our democratic process, then we all lose."
He will resume campaigning at an event in Cumbria later.
Analysis: By Tim Donovan, BBC London political editor
We were expecting the political day to be dominated by tax.
The weekend before polling day is one of the last opportunities to convey key messages on political talk shows - important when many voters are said to only engage in the last few days - before the exhausting final hours of the ground campaign ahead.
But instead, again, today has been about terror. Three attacks in three months. Two during the election campaign.
Debate might have lingered about whether or not to campaign, whether or not polling day should - even if it could - be postponed.
In fact there's been broad political unanimity that campaigning should resume as soon as possible after a time for reflection.
And there's been agreement that polling day should not be deferred. So the question now is how much events in London Bridge cloud the last four days of campaigning?
Will arguments over public services and Brexit be overshadowed now by concerns over policing, intelligence and community cohesion?
If so, it was possible to see - in the short formal responses of the leaders of the two main parties today - the ground on which this will be fought.
Jeremy Corbyn called for communities to come together, as they did in Manchester. "Our strength is the strength of our community unit."
Theresa May also said the country must "come together" but added qualifications.
This was the time for "embarrassing and difficult conversations" because there had been "far too much tolerance of extremism in our country", she said.
Election campaigning was paused for three days nearly two weeks ago after a suicide bomber killed 22 people at the Manchester Arena.
On 22 March, before the election campaign began, there was an attack on Westminster Bridge, by a man who drove into crowds and stabbed a policeman.
Five people were killed and the attacker was shot dead by police.
Scotland's First Minister Nicola Sturgeon said it was "right" to put the campaign on hold as "none of us have appetite for cut and thrust of politics when families are grieving and people are lying injured in hospital".
"It's right to resume the campaign tomorrow. We must have robust debate - our democracy is precious and we must make sure we safeguard it," she added.
Lib Dem leader Tim Farron said: "We must make sure we defend our country - that does not mean letting the pathetic cowards win, by us dismissing our democracy or getting rid of our freedoms."
Meanwhile Green Party co-leader Caroline Lucas said: "My heart goes out to all those affected and caught up in these horrific and despicable attacks, and my thoughts are with the victims and their families."
Explaining UKIP's decision to continue national campaigning, party leader Paul Nuttall said it was "time to start honouring our dead with more than just words".
"The only guarantee that will come from our choosing to stall the democratic process again will be more attacks - it is what these cowards want us to do."
He said he agreed with Mrs May that there had been "too much tolerance of extremism" and said she was using the "same language" as UKIP.
A special edition of BBC Question Time featuring the SNP's Nicola Sturgeon and Lib Dem Tim Farron was due to air on Sunday evening, but has been postponed to 21:00 BST on Monday.