His words were echoed by White House counter-terrorism adviser John Brennan, who told CNN: "It looks like he was working on behalf of the TTP, the Pakistani Taliban. This group is closely allied with al-Qaeda. This is something that we're taking very seriously."
If proved true, this would be the first time the Pakistani Taliban has been linked to a terror plot in the United States itself, the BBC's Madeleine Morris in Washington reports.
The bomb was discovered last Saturday evening in Times Square, which was busy with tourists and theatregoers at the time.
Bomb disposal experts were called in after a street-vendor noticed smoke coming from a Nissan Pathfinder, which had been left with its engine running and hazard lights flashing.
In the hours that followed, a claim of responsibility by the Pakistani Taliban was dismissed by the New York police. The city's Mayor, Michael Bloomberg, said there was no evidence the attempted bombing was the work of al-Qaeda or any other big terrorist group.
However, the unexploded bomb left crucial evidence intact that detectives used to trace Mr Shahzad.
He was arrested two days after the failed bomb attempt, trying to board a flight to Dubai from New York's JFK airport.
How Times Square bomb plotter was arrested
The trail which led to the arrest of Times Square bomb suspect began
with the discovery of a suspicious car early on Saturday evening, 1 May, close to New York's busy Times Square.
The Nissan Pathfinder was caught on cctv cameras arriving in Times
Square just before 1830 EDT. A street seller raised the alarm when he noticed the car parked with its engine running and hazard lights flashing.
Police evacuated Times Square. In the car's boot they found all the ingredients for a homemade bomb including propane gas cylinders, fireworks and two clocks, a metal gun locker containing fertiliser.
From the car's vehicle identification number, police traced the woman in Connecticut who sold the car to Faisal Shahzad (pictured). She also gave police a mobile phone number and helped identify him from photographs.
Faisal Shahzad lived in this Bridgeport building. Mobile phone records showed he made several calls to Pakistan and to a fireworks store in Pennsylvania. Court documents said he had received bomb-making training in Pakistan.
Police arrested Shahzad at 2345 EDT on Monday 3 May after he boarded a flight en route to Islamabad, Pakistan. Although his name was on a no-fly list, he had been allowed onto the plane.
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