Speaking at a news conference at the White House, Obama said Americans "stand with the people of Boston" and would pray for the victims and their families.
"We still do not know who did this or why, and people should not jump to conclusions before we have all the facts," Obama said. "But we will find out who did this and we'll find out why they did this. The responsible individuals and groups will feel the full weight of justice.
"We will find out who did this and we will hold them accountable."
Obama left the podium without taking questions.
Boston Police Commissioner Ed Davis said there were no warnings before two explosions ripped through crowds at the marathon, killing at least 3 people. WCVB-TV, Boston, reported one of the dead was an 8-year-old.
"There is no suspect at Brigham and Women's Hospital," Davis said at a Monday evening news conference. "There are people that we are talking to, but there is no suspect ... as has been widely reported in the press."
Massachusetts Gov. Deval Patrick said more than 100 people were injured, some of them "gravely."
"The city of Boston is open, and will be open tomorrow, but it will not be business as usual," Patrick said. "There will be a heightened law enforcement presence consistent with the severity and the seriousness of the ongoing investigation. People should expect, those who are riding the T, that there will be random checks of backpacks and other parcels, and we just ask everyone to be patient with that inconvenience for the time being. It is for the public's safety.
"We are also asking that everyone be on a state of heightened vigilance. That is really required of everyone. Please report suspicious packages or parcels or suspicious activity to local law enforcement."
Patrick said the FBI has taken charge of the investigation.
"This will be a combined federal, state and local effort," FBI Special Agent in Charge Richard DesLauriers said. "It will be an ongoing investigation. It is a criminal investigation that is a potential terrorist investigation."
DesLauriers also encouraged people in Boston to be on a heightened state of vigilance Monday night and Tuesday and to call 800-CALL-FBI with any tips. No other details were offered, and officials declined to say if any other potential explosive devices had been found.
U.S. Attorney Carmen M. Ortiz said there are "a lot of questions we wish we could answer at this point," adding the Justice Department does not wish to add to any misinformation that has been reported.
Davis said police were going through "all of the abandoned property that was discarded" in the area.
"We've pretty much cleared the Boylston Street area. There are no further devices that we've located at this point in time, but we are getting reports from various places about suspicious packages. That's perfectly understandable in this situation. I'm not prepared to say that we are ease at this point in time. We are still very actively pursuing every lead that we have," he said.
Obama said he had updated leaders of both parties in Congress and offered Boston and Massachusetts officials whatever federal resources they need to deal with the tragedy.
He said emergency workers and others "responded heroically and continue to do so as we speak without regard for their own safety."
"We salute all those who assisted and responded so quickly to this tragedy," Obama said.
"Boston is a tough and resilient town and so are its people. I'm confident they will pull together and move forward. The American people will be with them every single step of the way."
Davis, at an earlier news conference, indicated officials had found a third device and detonated it, but did not give details.
Davis later backed off an earlier report that there may have been a fourth incident involving a fire at the JFK library, saying it appeared "premature" to link it to the bombings.
Local reports said the fire in a mechanical room at the John F. Kennedy Presidential Library and Museum in the Dorchester neighborhood of Boston was quickly tamped down, but officials were investigating.
The two explosions at the Boston Marathon "occurred 50 to 100 yards apart" and "resulted in multiple causalities," Davis said.
"All the casualties have been removed from the scene," he said, but racers and spectators fleeing the scene left behind a large number of backpacks and other types of parcels, and investigators were methodically searching each one.
Asked if there were any warnings before the explosions, Davis said, "None."
Patrick said he received a phone call from Obama after the explosions, promising the full effort of the FBI.
A White House official said Obama received briefings from FBI Director Robert Mueller and Homeland Security Secretary Janet Napolitano on the active investigation and response to the incident, including the ongoing coordination with state and local officials.
At the Boston news conference, Davis said families of the victims could call a city line at 617-635-4500. Witnesses who want to talk to officials could call 800-494-TIPS.
He said officials did not yet know how many victims there were.
"People should remain calm but they should understand this is an ongoing event," Davis said. He asked people in Boston to stay at home and if they are visiting for the race, to return to their hotels and not congregate in large crowds.
Davis stopped short of calling the explosions bombs but said people can "draw your own conclusions."
Security has been tightened in New York and Washington as a precaution.
"This is a horrific day in Boston," Patrick said earlier.
"My thoughts and prayers are with those who have been injured," Patrick said in a statement. "I have been in touch with the president, Mayor [Thomas M.] Menino and our public safety leaders. Our focus is on making sure that the area around Copley Square is safe and secured. I am asking everyone to stay away from Copley Square and let the first responders do their jobs."
The first two blasts, which were about 15 seconds apart, occurred around 2:50 p.m., near the intersection of Boylston and Exeter streets where thousands of people were lined up to watch the 117th Boston Marathon.
The area was evacuated. The explosions occurred about 3 hours after the winners crossed the finish line. Video showed people trapped under scaffolding in the area.
The Boston Marathon follows a 26.2-mile course that winds through downtown Boston and outlying cities. An estimated 500,000 people come out to watch the race each year, The New York Times said.