Police said the device consisted of propane tanks, fireworks, petrol containers, wires and two clocks.
"The intent of whoever did this [was] to cause mayhem [and] create casualties," Kelly said.
Police have been examining the car and CCTV footage of the area in an attempt to identify who left the vehicle at the scene.
"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"
Kelly said a white man in his 40s had been identified on the footage and was seen removing a dark shirt to reveal a red shirt about half a block from the vehicle.
But he cautioned that there was no firm evidence to indicate that the man was linked to the car and the footage may be "innocent".
In addition to that footage, Kelly said a tourist had contacted police to say that he too "may have got a picture of the individual" caught in the frame while he was filming a nearby police officer.
The White House described the incident as "extremely serious" and said it was looking into all possible motives behind the attempted attack.
Robert Gibbs, the White House spokesman, said Barack Obama, the US president, spoke to the city's mayor about the incident and will speak publicly on the issue later on Sunday.
Earlier, Michael Bloomberg, New York's mayor, blamed the incident on "terrorists around the world", who want to take "freedoms" away from Americans.
But analysts told Al Jazeera that it was too early to blame the attempted attack on international "terrorists".
Riad Kahwaji, a security analyst from the Institute for Near East and Gulf Military Analysis in Dubai, said it would be "premature to jump to conclusions".
Mayor Bloomberg told the press: "We avoided what could have been a very deadly event"
"We have a precedent here, back in the 1990s, of the attack on the FBI building in Oklahoma city," he told Al Jazeera.
"People immediately accused Islamic militants and it turned out [the culprit] was one of the right-wing fundamentalists from inside the US.
"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, also 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 lifestyle 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."