Downing Street made the announcement after a night of chaos, with at least 48 in hospital after terrorists mowed down pedestrians before going on a knife rampage in Borough Market.
A spokesman said: “The Conservative party will not be campaigning nationally today.
“We will review as the day goes on and more emerge.”
Labour also announced they would but a break on national campaigning.
Theresa May and Jeremy Corbyn announced they have called off national election campaigning
Almost 50 people were injured in the attack
Leader Jeremy Corbyn said: “The Labour Party will be suspending national campaigning until this evening, after consultations with other parties, as a mark of respect for those who have died and suffered injury.”
In Scotland, the SNP, Tories, Lib Dems and Labour all announced they would suspend national campaigns.
Lib Dem leader Tim Farron said in a statement: “The election must go ahead as planned.
“It is right that we suspend our national campaigning for a short while out of respect for those affected by these tragic events, but local campaigning can and must continue.”
London Bridge terror: Scenes as armed police respond Sun, June 4, 2017
At least two people have died after being after reportedly being struck by a van on London Bridge on Saturday night.
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Armed police responding to the incident at London Bridge
The pre-election edition of BBC1's political programme The Andrew Marr Show was cancelled in response to the outrage.
However Ukip announced it would not suspend its General Election campaign.
Its leader, Paul Nuttall, said in a statement: "“It is 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.
All campaigning for the June 8 vote was called off for three days after a bombing in Manchester left 22 dead last month.
The Prime Minister will chair a meeting of the Government's Cobra emergency committee on Sunday in response to the tragedy.
Mrs May has come under pressure to postpone the General Election.
But London mayor Sadiq Khan said the vote should go ahead, saying he is "looking forward" to voting on Thursday.