The prime minister will chair a meeting of the Government's Cobra emergency committee on Sunday in response to the tragedy.
At least six people died and more than 48 were injured when three suspects ploughed a vehicle into pedestrians on London Bridge before attacking others in nearby tourist hotspot Borough Market.
Mrs May has since faced calls to cancel the election, due on June 8, particularly coming less than three weeks after the Manchester bombing.
Chris Cook, writing on Twitter, said: "We need to cancel or postpone this election.
"It is impossible to have an unbiased campaign when our news is being dominated by terrorism."
Roy Shepherdson added: "The General Election IS the target. Can't let them win. Postpone it a week."
And Nick Applewhite said: "Something must be done to postpone election. Third attack in three months is horrifying."
In 2001, Tony Blair had to postpone an entire election by a month because of an outbreak of foot-and-mouth disease.
Mr Blair had let it be known that he had pencilled in the election for May 3 to coincide with local council polls, but delayed the votes until June 7 because of the difficulty of campaigning while the animal disease was being contained.