"I would like to appeal to the families, friends and sympathisers of Christopher Coke to remain calm," Owen Ellington, the police commissioner, said on Tuesday.
Police arrested Coke at a road checkpoint in the Portmore area of St Catherine Parish on the outskirts of Kingston on Tuesday.
He is expected to make his first court appearance within 48 hours, Daryl Vaz, the Jamaican information minister, said.
Ellington said that Coke was in good condition when he was arrested but provided few specifics saying that "the circumstances of [Coke's] arrest are being investigated".
But Al Miller, an influential evangelical preacher who facilitated the surrender of Coke's brother earlier this month, told the Associated Press news agency that Coke was prepared to surrender to officials at the US embassy in Kingston when police stopped his vehicle on a highway outside Kingston.
"A contact was made on his behalf that he wanted to give himself in," Miller said.
"I therefore made arrangements with his lawyers because he wanted to go ahead with the extradition process, so we communicated with the US embassy because that's where he would feel more comfortable."
Miller, a minister at the nondenominational Whole Life Ministry, said after capturing Coke, police took him to the nearby Spanish Town police headquarters.
He said Coke contacted him to ask his help in arranging the surrender at the embassy because he did not trust the police not to harm him if he surrendered to them.
"He also wanted to waive his right to an extradition hearing so that he could go to the US for a trial," Miller said.
Coke's father died in a mysterious prison fire while he was awaiting extradition.
Coke was known as "president" to the people of the Tivoli Gardens slum, and served as community leader and enforcer in the neighbourhood in an area that the government acknowledges it has long neglected.
"When people go to the police to make complaints, the police just say 'Go home, we'll come see you soon'," Everton Cornpipe Jones, Coke's brother, told Al Jazeera.
"But they never come and then anything can happen to you."
Coke also commanded a private militia and was a strong supporter of the ruling Jamaica Labour party.
US prosecutors have described Coke as the current leader of the "Shower Posse" that murdered hundreds of people by showering them with bullets during the cocaine wars of the 1980s.
Describing the latest developments, Ross Sheil, a journalist with the Observer newspaper, told Al Jazeera: "This has come at the end of what has been a very turbulent month for Jamaica, so people are generally very relieved."
He said the extradition process "could play out in the next 48 hours".
Vaz, the information minister, said authorities have not confirmed reports that Coke does not want to fight extradition to the US.
Jamaica initially refused requests to extradite him to New York for trial after his indictment last year, and the case had strained relations between the US and Jamaica.
Coke faces life in prison if convicted.