British Prime Minister David Cameron wrote on Twitter that footage from the blasts was "shocking and horrific", and said that his thoughts were with those affected.
The harrowing scenes of injured spectators quickly prompted fears of a similar incident at the London race.
"We will not be cancelling, what we are doing, we are reviewing," London Marathon Chief Executive Nick Bitel told BBC Radio 5 Live.
"You look at what has occurred, if there are steps we can take to increase security and all sorts of measures one could deploy.
"We run through the city, when you have an event of any nature, a marathon, parade, it's only as safe as the city itself, if it's not held in a stadium you can't do a lockdown like you may do in a building," he added.
Thousands of people, including leading international athletes, compete in the London Marathon every year and, with the race just six days away, there was earlier speculation the event could be cancelled on safety grounds.
Bitel said he was "deeply saddened and shocked by the news.
"Our immediate thoughts are with the people there and their families," he said in a statement. "It is a very sad day for athletics and for our friends and colleagues in marathon running.
"Our security plan is developed jointly with the Metropolitan Police and we were in contact with them as soon as we heard the news."
Met Police Chief Superintendent Julia Pendry added: "A security plan is in place for the London Marathon. We will be reviewing our security arrangements in partnership with London Marathon."
The explosions in Boston took place after the elite race had finished.
Lelisa Desisa of Ethiopa won the men's race with Rita Jeptoo winning the women's event.
British Foreign Secretary William Hague said he was "appalled by news" while Irish Prime Minister Enda Kenny offered his sympathy to the people of Boston, a city with strong Irish roots.
"On behalf of the Irish people, I am sending our sympathy and support to Mayor Menino and Governor Patrick and to the people of Boston who have been devastated by this senseless and terrible event," he said.
"Our thoughts and prayers are with the victims and their families."
Scottish First Minister Alex Salmond also offered his sympathies.
"I am sure that the thoughts of the people of Scotland will be with our close friends in Boston as they come to terms with the terrible events unfolding in their city.
"The ties that bind Scotland and the United States are strong and deep.
"It is almost unthinkable that such a tragedy could unfold at a similar, family-friendly race event in the United States," he added.
Paula Radcliffe, the British women's marathon world record holder, said she was "horrified to hear news".
"Really hope there are no serious casualties. Situation looks awful, thoughts with everyone. There are some very sick people out there, who would do something like this?"
Competitor Abi Griffiths, one of more than 370 British athletes officially competing in the event, completed the race 10 minutes before the explosions and explained that it was immediately clear something was wrong.
"There is a protocol when you finish a marathon -- first of all you just want to fall on your hands and knees because it is just so exhausting," she told Sky News.
"It was while I was getting my bag that I heard it go off.
"The ground shook and immediately people sort of looked around -- it was just too loud to be something that wasn't serious."
The Boston race, the world's oldest annual Marathon, is held each year on the United States' Patriots' Day.