"We have no idea who did this and why," he said.
'Potential terrorist attack'
Bomb-squad staff were deployed in the busy square in the heart of Manhattan late on Saturday and police shut down several streets after a T-shirt vendor, who saw smoke emerging from the car, alerted police.
Mayor Bloomberg told the press: "We avoided what could have been a very deadly event"
There were reports of a small flash and popping sounds also coming from the car.
"We are treating it as if it could be a potential terrorist attack," Janet Napolitano, the homeland security secretary, said on Sunday morning.
The square was reopened after car had been removed.
Bloomberg said that "terrorists around the world", who want to take "freedoms" away from the Americans, always focus on the symbol of those freedoms - New York city.
The car was towed by police to a forensic facility in Jamaica, Queens, where investigators are searching for fingerprints and other DNA evidence.
No prints have yet been found, officials said, but the analysis is still in its early stages.
Riad Kahwaji, a security analyst from the Institute for Near East and Gulf Military Analysis in Dubai, said it was "premature" to accuse international terrorists.
"We shouldn't jump into conclusions here," he told Al Jazeera.
"We have a precedent here, back in the 1990s, of the attack on the FBI building in Oklahoma city. People immediately accused Islamic militants and it turned out [the culprit] was one of the right-wing fundamentalists from inside the US.
"I've spoken to Islamists for
20 years. They don't give a jot about my life style in the United Kingdom or what goes on in America."
Phil Rees, author
"Right now, the big bogeyman is al-Qaeda, the Islamic terrorists. ... For the US, it's always safe and good for their own political advantage to accuse the Islamic militants even if it turned out that they have nothing to do with it."
Phil Rees, the author of Dining with Terrorists, dismissed Bloomberg's comments about terrorists targeting American freedoms.
"I've spoken to Islamists for 20 years. They don't give a jot about my life style in the United Kingdom or what goes on in America," he told Al Jazeera.
"They care about American foreign policy, what the United States is doing in Muslim lands, not just in Iraq and Afghanistan, but the way it has corrupted many Muslim leaders, the way that it prevents democracy emerging in Muslim lands, the way that it obviously doesn't look at Palestine and Israel in equal terms."
A statement issued by the White House said the New York police department had done "excellent work" in responding to the incident.
Unconfirmed reports said someone had been seen running from the car.
The vehicle had been parked close to a theatre on the corner of 45th Street and Seventh Avenue.
Times Square is one of the city's most high-profile attractions and police are deployed there in large numbers. In December, they closed the area while inspecting a van at first feared to contain a bomb, but which turned out to be carrying nothing dangerous.