In his second public statement in less than 24 hours since the explosions, the president said, "Clearly we are at the beginning of our investigation." He urged anyone with information relating to the events to contact authorities.
Obama said investigators "don't have a sense of motivation yet" as they begin to evaluate the attack in which three people were killed, including an 8-year-old boy, and more than 170 were wounded.
Despite the loss of life and limb, Obama declared, "The American people refuse to be terrorized."
As he had on Monday, he said those responsible for the attacks would be brought to justice.
The president had avoided labeling the incident a terrorist attack when he stood at the same White House lectern shortly after the explosions, but lawmakers quickly said that's what it was. White House officials had said the FBI was investigating the attack as a terror incident.
Appearing before reporters on Tuesday, Obama said the events in Boston were a "heinous cowardly act, and given what we now know about what took place, the FBI is investigating it as an act of terrorism. Any time bombs are used to attack innocent civilians it is" a terrorist act, he said. Still, he cautioned that it was not known who or what organizations might have carried it out.
The president praised those who had come to the aid of the injured.
"If you want to know who we are, what America is, how we respond to evil, that's it: selflessly, compassionately, unafraid," he said.
Obama stepped to the microphone after receiving a briefing at the White House from Attorney General Eric Holder, Homeland Security Secretary Janet Napolitano and other top aides.
The bombs exploded on Monday afternoon near the finish line of the famed Boston Marathon, an annual 26 mile race through the neighborhoods of the city.