Speaking hours after a suspect was pulled off a plane about to depart for the Middle East, Obama said "justice will be done" in the incident.
The president said "hundreds of lives" may have been saved through quick action by ordinary citizens and local, state and federal authorities on Saturday night.
"We know that the aim of those who try to carry out" attacks like the one last weekend is to force Americans to live in fear, Obama said.
"As Americans and as a nation, we will not be terrorized. We will not cower in fear. We will not be intimidated," he vowed.
Obama said, "The American people can be assured that the FBI and their partners in this process have all the tools that they need to learn everything that we can, and that includes what, if any, ties this individual has to individual groups."
The president made his comments at the annual meeting of the Business Council.
Earlier, spokesman Robert Gibbs told reporters that Obama had been informed a few minutes after midnight about the arrest of a suspect, Faisal Shahzad.
Shahzad, a Pakistan-born U.S. citizen, is suspected of driving a bomb-laden SUV into Times Square last Saturday and parking it on a street lined with restaurants and Broadway theaters. He was expected in court to face charges that he tried to set off a massive fireball and kill Americans, federal authorities said.
Shahzad, was taken into custody late Monday by FBI agents and New York Police Department detectives at Kennedy Airport after he boarded a flight to Dubai, according to officials.
Obama telephoned two New York City police officers, Wayne Rhatigan and Pam Duffy, Tuesday morning to thank them for their vigilance. The officers were in Times Square Saturday night, and are credited with evacuating the area after the suspicious vehicle was spotted. Obama also spoke Tuesday with Lance Orton, a street vendor who first reported the vehicle. The president called another vendor who reported the vehicle, Duane Jackson, on Monday.
The incident marked the second time in recent months in which terrorists evidently sought to wreak havoc in the United States.
Umar Farouk Abdulmutallab is in custody on charges of trying to use a bomb hidden in his underwear to bring down a Detroit-bound airliner on Christmas Day.