Scores were injured, many suffering shrapnel wounds, in the two blasts which rocked the finish line.
Massachusetts General Hospital said "several amputations" had to be performed on survivors.
Police were searching a flat in the Boston suburb of Revere as part of the investigation. Massachusetts State Police confirmed that a search warrant was served last night but gave no more details.
There were no immediate claims of responsibility for the terror attack, the most serious in the US since the 9/11 World Trade Centre atrocity. Al Qaida-linked groups and militant white extremists have attacked targets in America in the past.
President Barack Obama, speaking from the White House, avoided using the words "terror" or "terrorism", saying officials "still do not know who did this or why".
In a televised address, he said those responsible will feel the "full weight of justice".
However, a White House official later said the explosions at one of the world's oldest and most prestigious marathons was being treated as terrorism.
Bill Bratton, a former head of Boston police who is now based in London, said: "Unfortunately in my country there are no shortage of potential suspects, if you will."
He told Sky News there had been no warning that an attack may have been imminent.
"To the best of my understanding and from my sources there was no sense that there was going to be anything occurring at that marathon."
Asked about the potential threat to Baroness Thatcher's funeral tomorrow and the London Marathon this weekend, he said: "Needless to say, nobody does it better than British police services in policing these kinds of events.
"You've had all too many experiences with the actual attacks, so certainly security will be ramped up from the already extraordinarily high levels originally planned for these events."
He said there would be a "determined effort" to find those responsible and bring them to justice, adding: "America, like Great Britain, is resilient and will not cower in the face of terrorism."
Horrifying images of injured spectators and blood-spattered pavements were caught as television cameras broadcast footage of the explosions.
Participants were also seen lying on the ground as the impact tore through the finish line, sending smoke and debris soaring into the air.
Emergency workers ripped away fencing as others carried injured men and women from the scene.
A list of competitors on the Boston Marathon website showed hundreds of British and Irish runners were expected to line up for the race.
Prime Minister David Cameron led politicians in tweeting their solidarity with those affected, saying: "The scenes from Boston are shocking and horrific - my thoughts are with all those who have been affected."
Security for the London Marathon on Sunday will be reviewed following the explosions, Metropolitan Police Chief Superintendent Julia Pendry, the event commander for the race, said.
Sports Minister Hugh Robertson insisted he was "absolutely confident" that the London event could be kept safe.
Asked if he believed it should still go ahead, he told the BBC Radio 4 Today programme: "Yes, I do.
"These are balance of judgments but we are absolutely confident here that we can keep the event safe and secure.
"I think this is one of those incidents where the best way to show solidarity with Boston is to continue and send a very clear message to those responsible..."
Nick Bitel, the chief executive of London Marathon, said: "We are deeply saddened and shocked by the news from Boston.
"Our immediate thoughts are with the people there and their families. 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."
The Boston Marathon is held each year on Patriots' Day.
Ed Davis, the city's Police Commissioner, said there had been two "simultaneous explosions" near the finish line of the 26.2-mile event.
"Each scene resulted in multiple casualties," he told a press conference.
The first explosion occurred just before the photo bridge that marks the finish line. The second explosion could be heard a few seconds later.
They occurred about four hours into the race, a time when large numbers of runners would be finishing, with many more relatives and friends cheering them on.
As many as two unexploded bombs were also found near the end of the course as part of what appeared to be a well-co-ordinated attack, but they were safely disarmed, according to a senior US intelligence official.
London Mayor Boris Johnson has spoken to Metropolitan Police Commissioner Sir Bernard Hogan-Howe about the possibility of extra security for the London Marathon.
Mr Johnson said: "The bombings in Boston are shocking, cowardly and horrific, and the thoughts of all Londoners this morning will be with the victims. Boston is a proud city built on history, tradition and a real sense of community.
"These attacks were aimed at its core, at innocent men, women and children enjoying a spring day out at a major sporting event.
"We do have robust security measures in place for Sunday's London Marathon but, given events in Boston, it's only prudent for the police and the organisers of Sunday's race to re-examine those security arrangements."
Mo Farah, the double Olympic champion, retweeted a message from the charitable foundation he set up which said: "The @FarahFoundation is thinking of all those in Boston today xx."
Paula Radcliffe, the women's marathon world record holder, posted on Twitter: "Situation looks awful, thoughts with everyone. There are some very sick people out there, who would do something like this?