At least three people were killed and more than 140 injured by the blasts near the finish of the Boston Marathon.
Sports Minister Hugh Robertson said he was “absolutely confident” the London Marathon could be kept safe.
London had “enormous experience” of delivering major events and the UK had some of the best security professionals in the world, he said.
Hugh Robertson added: “This is one of those instances where the best way to show solidarity with Boston is to continue.”
Home Secretary Theresa May has been briefed on the bombings by Scotland Yard Assistant Commissioner Cressida Dick and MI5 chief Sir Jonathan Evans.
At this stage, there are no plans for a meeting of the UK government’s emergency committee Cobra, but high-level discussions were already planned and will go ahead because of Margaret Thatcher’s funeral on Wednesday, April 17.
The Metropolitan Police said security for the funeral in central London would not be affected by the Boston Marathon explosions and that it was a very different event.
London Marathon chief executive Nick Bitel said in a statement: “We are deeply saddened and shocked by the news from Boston.”
He later said he “fully expected” the London Marathon, which first took place in 1981 and was completed by more than 37,000 people last year, to go ahead.
Nick Bitel said security plans “take account of many contingencies, including this type of threat and incident, but one can’t be complacent and when it has happened, you need to then review those plans you have in place to see what else may be necessary.”
St James’s Palace said Prince Harry would still attend the marathon to make the presentations to the winners.
The London Marathon route, which is lined by hundreds of thousands of spectators every year, starts in Blackheath and finishes near Buckingham Palace, passing some of the capital’s most recognisable landmarks including Tower Bridge, Canary Wharf and Big Ben.
London Mayor Boris Johnson described Boston Marathon bombings as “shocking, cowardly and horrific”.
He has spoken to Met Police Commissioner Sir Bernard Hogan-Howe about the possibility of extra security for the London Marathon.
“We do have robust security measures in place, but given events in Boston it’s only prudent for the police and the organizers of Sunday’s race to re-examine those security arrangements,” he said.
British police say they have also launched a review of security for the Greater Manchester Marathon, due to take place on Sunday, April 28.
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