Boston police say officers are working around the clock and all leave has been cancelled.
At least 17 people are critically wounded, officials say, and the injuries include several amputations.
One of the dead was an eight-year-old boy, US media said.
In a televised address, President Barack Obama vowed to bring those behind the attack to justice.
“We will find out who did this. We’ll find out why they did this,” the president said.
“Any responsible individuals, any responsible groups, will feel the full weight of justice.”
Although President Barack Obama did not use the word “terrorism”, a White House official later said: “Any event with multiple explosive devices – as this appears to be – is clearly an act of terror, and will be approached as an act of terror.”
The first explosion came at about 14:50 local time on the north side of Boylston Street, about two hours after the winners crossed the line.
There was initial confusion and panic. Some runners fell to the floor while police and bystanders ran to help those caught in the blast.
Then seconds later, another explosion ripped into the crowd further away from the finishing line, between 50 and 100 metres from the first blast.
TV footage showed bloodied runners and spectators being treated at the scene and the road strewn with debris. Rescuers tore down temporary fencing to reach the casualties.
Medical officials speak of at least 140 injured, with injuries including severed limbs, shrapnel wounds, cuts and bruises.
At an initial news conference, Boston Police Commissioner Edward Davis said authorities had received “no specific intelligence that anything was going to happen”.
He urged people to stay indoors and not congregate in large groups.
At a second news conference he said the death toll now stood at three. He said that no suspects were in custody.
A search thought to be related to the inquiry was under way at a flat in a Boston suburb, Boston media reported.
Police said a search warrant was issued on Monday in the Revere district but provided no further details.
Massachusetts Governor Deval Patrick said Boston would be “open” on Tuesday but that there would be “a heightened law enforcement presence”.
“There will be random checks of backpacks and other parcels. We are also asking that everyone be on a state of heightened vigilance,” he said.
FBI Special Agent Richard DesLauriers also appeared, saying that the inquiry involved city, state and federal officials, but refusing to give any details of the investigation.
Details of the victims have also not been revealed, however an 8-year-old boy is said to be among the dead. Quoting a family friend, Associated Press said the boy’s mother and sister were also injured as they waited for his father to finish the race.
Officers have already begun poring over video and photographs from the marathon.
Two other unexploded devices were reported to have been found near the end of the race but were safely defused.
State police officer Roupen Bastajian had just finished the race when he heard the blasts.
“I started running toward the blast and there were people all over the floor,” he said.
“We started grabbing tourniquets and started tying legs. At least 25 to 30 people have at least one leg missing, or an ankle missing, or two legs missing.”
A doctor at Massachusetts General Hospital said “several amputations” had been performed there.
As a massive security operation swung into operation, the Federal Aviation Administration barred low-flying aircraft from within 3.5 miles of the site.
Key sites in Washington DC and New York have also seen security tightened.
Officials in Washington said no group or individual had so far said they carried out the attack.
Shortly after the blasts, a fire broke out at Boston’s JFK Library a few miles away from the explosions.
Police said the blaze might have been caused by an incendiary device but it is unclear whether it is related to the explosions.
The annual Boston Marathon this year had a field of about 23,000 runners and was watched by hundreds of thousands of spectators.
Boston Marathon is held on Patriots Day, a Massachusetts state holiday which commemorates the first battles of the American Revolution in 1775.
Meanwhile British police are reviewing security plans for Sunday’s London Marathon, the next major international marathon, following events in Boston.
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