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. 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.