Michael Bloomberg said Dzhokhar Tsarnaev, the surviving suspect, had told the FBI he and his brother Tamerlan “spontaneously” decided that New York would be next.
Police Commissioner Raymond Kelly told reporters the suspects had a pressure cooker bomb and five pipe bombs.
Three people died and over 260 were wounded in the April 15 Boston Marathon attack.
“Last night we were informed by the FBI that the surviving attacker revealed that New York City was next on their list of targets,” Michael Bloomberg said during Thursday’s news conference at city hall.
“He and his older brother intended to drive to New York and detonate those explosives in Times Square.”
Raymond Kelly said the brothers had planned to head to New York after hijacking a car and its driver in Boston last Thursday night.
“That plan, however, fell apart when they realized that the vehicle they hijacked was low on gas and ordered the driver to stop at a nearby gas station,” Raymond Kelly said, adding that the driver escaped and alerted police.
Police intercepted the brothers in the stolen car, prompting a gun battle that left 26-year-old Tamerlan Tsarnaev dead.
Michael Bloomberg praised Massachusetts law enforcement for their work in stopping the suspects, saying “we know they had the capacity to carry out the attacks”.
Dzhokhar Tsarnaev, 19, is said to have travelled to New York at least once last autumn.
He is now in police custody in hospital and has been charged with using a weapon of mass destruction to kill people.
Before reportedly telling investigators he and his brother planned an attack on Times Square, Dzhokhar Tsarnaev had said they were planning to go to New York “to party” after the bombings.
Following 16 hours of interrogation, Dzhokhar Tsarnaev stopped responding to investigators’ questions after being read his legal rights to remain silent and have a lawyer, US media report.
Michael Bloomberg said there was no evidence New York was currently a target, but that the Tsarnaevs’ alleged plan proved the city remained a prime location for people who want to “bomb and kill Americans”.
On Thursday afternoon, police vehicles lined Times Square in a show of force, with officers standing shoulder to shoulder.
“Why are they standing like that? This is supposed to make me feel safer?” Elisabeth Bennecib, a tourist from France, told the Associated Press.
“It makes me feel more anxious, like something bad is about to happen.”
The suspects’ father, Anzor Tsarnaev, has said he will travel imminently to the US. The family wants to take Tamerlan’s body back to Russia. But it is not clear if his former wife will join him.
Zubeidat Tsarnaeva left the US and failed to make a court appearance after being arrested last June on suspicion of stealing $1,624 of women’s dresses from a Massachusetts department store.
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