One sequence of film showed "a white male in his 40s" who Raymond Kelly, the city police chief, said was acting in a "furtive" manner and changing his clothes as he walked away from the area.
The police said the man was a "person of interest".
The bomb, which was discovered after a street vendor saw smoke coming out of a parked car, prompted the evacuation of thousands of people from the square and surrounding areas on Saturday evening.
Kelly said the amateurish device, had it exploded, would have created a "significant fireball."
The car "would have at least have been cut in half", he said.
Kelly dismissed a claim of responsibility made over the internet by the Pakistani Taliban.
Pakistani Taliban sources told Al Jazeera that they were not involved.
But later on Sunday, videotapes purportedly showing Hakimullah Mehsud, the leader of the Pakistani Taliban, talking about attacks in the US, were released by SITE, a US-based agency that monitors Taliban media.
In one video, an unidentified voice described by SITE as Mehsud speaking in Urdu, says that the Pakistani Taliban takes "full responsibility for the recent attack in the USA".
No specific reference
The video, allegedly recorded on April 19, makes no specific reference to the attack in New York City, nor does it mention that the location or that it was a car bomb.
Mehsud was presumed to have been killed in a drone strike in northwestern Pakistan on January 14.
But last week Pakistani intelligence officials suggested Mehsud may have survived the attack.
In a separate recording, released by IntelCenter, another monitoring agency, a man appearing to be Mehsud promises that "God willing, very soon in some days or a month's time, the Muslim [community] will see the fruits of most successful attacks of our fedayeen in USA".
"Fedayeen" usually refers to suicide bombers, which the car bomb attempt in New York did not involve.
Al Jazeera's Kamal Hyder, reporting from the Pakistani capital, Islamabad, said the threat apparently issued by Mehsud could have ramifications both in the US and in Pakistan.
"Will they [the US] increase the number of drone strikes into Pakistan now that Hakimullah has issued a threat?" he said.
"The claim that there will be suicide attacks in mainland USA is not something the Americans will take lightly. They will, of course, update security operations.
"The question is if the Taliban has the capability to strike on such a large distance. It's not something that many people believe is possible."
Baitullah Mehsud, the predecessor of Hakimullah Mehsud, reportedly claimed responsibility for a mass shooting at the American Civic Association in Binghamton in April 2009. That claim turned out to be false.