Kelly's warning came in the wake of the arrest of Quazi Mohammad Rezwanul Ahsan Nafis, 21, a Bangladeshi national who allegedly wanted to "destroy America" by blowing up the Federal Reserve Bank of New York.
Nafis, described as having a connection to al-Qaida, was arrested after he allegedly tried to set off a fake 1,000-pound bomb in a sting operation conducted by the New York FBI Field Office's Joint Terrorism Task Force and New York police.
Kelly said al-Qaida operatives and those they have inspired have "tried time and again to make New York City their killing field."
He said prior to Wednesday's incident, authorities had discovered 15 plots since the Sept. 11, 2001, terrorist attacks on New York and Washington.
"After 11 years without a successful attack, it's understandable if the public becomes complacent. But that's a luxury law enforcement can't afford," he said, adding vigilance will always remain the department's watchword.
Assistant FBI Director Mary Galligan said attempting to destroy a landmark building and kill or maim untold numbers of innocent bystanders "is about as serious as the imagination can conjure."
"It is important to emphasize that the public was never at risk in this case, because two of the defendant's 'accomplices' were actually an FBI source and an FBI undercover agent," she said.
The criminal complaint against Nafis, who has been charged with conspiring to use weapons of mass destruction and providing material support to al-Qaida, said he arrived in the United States in January on a student visa and tried to recruit people to form a terrorist cell to help him carry out his attack.
Nafis, who faces life in prison if convicted, also allegedly wanted to kill President Obama, The New York Times, quoting a senior law enforcement official, reported.
The report said Nafis, as described in court paper, had been eager to win al-Qaida's respect.
The undercover agent reportedly had been working with Nafis since July and had been recording the suspect's statements. The suspect is reported to have said: "I don't want something that's like, small. I just want something big. Very, very, very, very big, that will shake the whole country."
In a video statement, which Nafis allegedly recorded prior to trying to detonate the explosive, he said: "We will not stop until we attain victory or martyrdom."
Britain's Daily Telegraph said Nafis also reportedly told FBI agents he was inspired by the videos of Anwar al-Awlaki, an extremist who sent out hate sermons online. Awlaki, raised in the United States, was killed last year in a drone strike in Yemen.
The Los Angeles Times said Nafis had stayed in a Queens apartment as he allegedly sought to recruit militants.
Before deciding on the Federal Reserve Bank for attack, Nafis allegedly had thought of other targets, including the New York Stock Exchange. But the bank was chosen as Nafis explained in a piece to be sent to an online militant magazine because it was the most influential of all the regional Federal Reserve banks, the LA Times said.