John J. Miller, the New York Police Department’s deputy commissioner of intelligence and counterterrorism, said both the F.B.I. and Justice Department were aware of the case, believed to be the N.Y.P.D.’s first international terrorism prosecution. Neither raised objections.

Mr. Miller declined to comment on whether Mr. Faisal had ties to other governments. The F.B.I. also declined to discuss Mr. Faisal.

In the last decade, Mr. Faisal’s name has surfaced repeatedly in terrorism cases. He was close to one of the suicide bombers in the 2005 London bombings that killed 52 people. Najibullah Zazi, who was convicted of trying to blow up the New York City subways in 2009 as part of an Al Qaeda plot, listened to his sermons condoning suicide bombings. His influence has been seen in an outsized flow of ISIS recruits from Trinidad and Tobago.

His name has been linked to three Islamic State terrorism prosecutions in New York, Arizona and Philadelphia, where he was in touch with a mother of three who was eventually arrested for trying to join the Islamic State. F.B.I. agents found CDs of Mr. Faisal’s lectures in the apartment of two men killed in Texas in 2015 when they attacked an exhibition of cartoons depicting the Prophet Muhammad.

Most recently, the F.B.I. on Monday arrested a young man named Parveg Ahmed, 22, of Queens, and charged him with attempting to travel to Syria to fight for the Islamic State. An F.B.I. search of his computer revealed that he had been listening to lectures by Mr. Faisal, including one entitled: “The 9 Reasons Why the Kuffar Hate the Believers.” Kuffar is a derogatory term for non-Muslims.

According to Mr. Morton, Mr. Faisal had a considerable following in Jamaica, where he once debated a bishop on a television show called “Religious Hardtalk.” A spokeswoman for Jamaica’s Ministry of National Security, Akierah Binns, declined to comment on the extradition proceedings.

Mr. Faisal, 53, was born Trevor William Forrest in Jamaica and took his Muslim name after converting to Islam as a teenager. He studied in Saudi Arabia and first came to public attention while working in London as an imam, known as Sheikh Faisal, after the Sept. 11, 2001, terrorist attacks. British press reports said that on cassette tapes distributed in London shops at the time, he urged young Muslim men to train for jihad.