The president called the bombing "a heinous and cowardly act" used to target innocent civilians. He urged anyone with information about the attack to contact authorities.
"Given what we now know about what took place, the FBI is investigating it as an act of terrorism," Mr. Obama said. "Anytime bombs are used to target innocent civilians, it is an act of terror."
On Tuesday night, a candlelight vigil was held in Boston for the victims. Hundreds of people sang and held candles in the streets, moving from a historic church to a nearby park.
"My young people really needed to be together tonight, so I would guess we had about 700 people in there tonight just gathered and singing and praying," said Kim Crawford Harvey, a minister, "just being together reaffirming that life will go on in this city."
The two bombs that stunned Boston Marathon runners and spectators appear to be packed with ball bearings, nails and other metal fragments, according to investigators. Officials recovered a circuit board or parts of circuit board from one of the bombs. The recovered remains of one of the bombs has been described as a mangled, medium-sized pressure cooker.
"This morning, it was determined that both of the explosives were placed in a dark-colored nylon bag or backpack," FBI Special Agent Rick DesLauriers said. "The bag would have been heavy because of the components to be in it."
Massachusetts Gov. Deval Patrick said no unexploded bombs were found and that the only explosives were the two that went off. According to experts, ball bearings found in victims' bodies suggest the bombs were designed to scatter shrapnel.
The attack killed three people and injured more than 170 people. One of the injured is a man from Southern California. He was in critical condition.
One of the three people killed in the bombings was identified as 29-year-old Krystle Campbell of Medford, Mass. A second victim, whose name was withheld, was a Boston University graduate student from China, according to the Chinese consulate general in New York.
The third victim was an 8-year-old boy identified as Martin Richard. He was with his mother and sister, waiting to see his father cross the finish line. Officials said at least 10 children were being treated for their injuries at area hospitals.
Investigators are tracking multiple persons of interest, including a man being treated at an area hospital and another individual who was seen trying to gain access into a restricted area five minutes before the bombings.
The investigation led dozens of officers to a fifth-floor apartment building in Revere, just north of Boston, Monday night. One tenant said an agent from the Bureau of Alcohol, Tobacco, Firearms and Explosives told him they were acting on a tip and looking for a dangerous device. Authorities searched the unit for eight and a half hours. It was unclear if they found anything.
So far, no motive has been released and no one has claimed responsibility for the attacks.
"It could be a group but one person could easily have done something like this," said Kevin Miles, who was a top explosives expert for the FBI until retiring a few months ago.
Police were highly visible across Boston on Tuesday, many armed with assault weapons.
Los Angeles resident Jennifer Hartman made her own medal for finishing 26.1 miles of the race. She was .1 miles away from the finish line when she felt the explosion.
"The immediate moment to me was just, 9/11. It was the cloud of smoke coming out, some people were running, some people were crying," Hartman said.
Bill Iffrig, a 78-year-old man in the race, described how he was knocked down to the ground as he approached the finish line.
"I got down to within about 15 feet of the finishing apron and just tremendous explosion, sounded like a bomb went off right next to me," Iffrig said. "The shock waves just hit my whole body and my legs just started jittering around. I knew I was going down."
President Obama planned to be in Boston on Thursday to attend a service for the victims.
In response to the bombings, major U.S. cities are on heightened alert and bolstering security at sporting events and major gatherings.