A senior party spokesman said national events were being suspended on Sunday and a decision on further campaigning would be taken later in the day.
It is the second time the campaign for the June 8 poll has been interrupted by atrocities, following a three day pause after the suicide bomb attack in Manchester.
The Tory spokesman said: “The Conservative party will not be campaigning nationally today. We will review as the day goes on and as more details of the attack emerge.”
Prime Minister Theresa May was returning to Whitehall to meet senior ministers and security chiefs in the Government’s emergency Cobra committee.
Mrs May said: “Our thoughts are with those who are caught up in these dreadful events.”
The London Bridge attack, which killed six and injured at least 48, was met by an outpouring of messages from candidates in the election, of sympathy for those affected and praise for the response of the emergency services.
A number of senior politcians urged Mrs May to resist calls to delay the election in response to the tragedy.
Conservative former foreign minister Alistair Burt said: “We don’t have a Parliament or MPs at present. If there’s no general election, when would we get one?
“Must carry on. Parliament must be the national forum to decide response. We cannot live by incident and reaction via vox pop and social media.”
The Democratic Unionist Party’s Jeffrey Donaldson said the election should “absolutely not” be delayed: “If we suspend our democratic process it feeds the warped belief of the terrorists that they can win. We need Parliament back.”
The attack came five days before the election, with opinion polls suggesting great uncertainty about the outcome of the contest.
One new opinion poll by Survation for the Mail on Sunday put Conservatives a single point ahead of Labour, on 40% to 39% for Jeremy Corbyn’s party.
However the findings contrast sharply with a ComRes poll for the Independent and Sunday Mirror which still shows the Conservatives with a 12-point advantage.
Opinium for The Observer also has the Tories ahead but with the gap narrowing to six points.
Mr Corbyn condemned the “brutal and shocking incidents” in London, adding: “My thoughts are with the victims and their families. Thank you to the emergency services.”
Liberal Democrat leader Tim Farron said: “Tonight’s horrific incidents in London remind us how much we owe our emergency services. My thoughts and prayers with everyone affected.”
Scottish National Party leader Nicola Sturgeon said: “Dreadful news from London. My thoughts are with all those affected.”
Plaid Cymru’s Leanne Wood said: “This is another devastating attack. Plaid Cymru extends its condolences to the people affected and the emergency services that work so hard in these difficult circumstances. People deserve to live their lives without fear, and we must come together to reject hate.”