The Obama administration and a US presidential hopeful have criticised Sean Penn's interview with Mexican drug kingpin Joaquin "El Chapo" Guzman.
It was conducted in October in the Mexican jungle after Guzman's jail break, and published by Rolling Stone.
A White House spokesman said Guzman's boasts about his exploits were "maddening", and Republican Marco Rubio said the interview was "grotesque".
Guzman, 58, was recaptured on Friday after months on the run.
Unnamed Mexican officials say Penn's secret meeting helped lead them to the boss of the Sinaloa drug cartel.
He has now been returned to the maximum-security Altiplano jail, from where he escaped in July via a tunnel dug to the shower in his cell.
Social media reaction
Twitter users were quick to offer their verdict on the interview:
In the Rolling Stone article, the result of a seven-hour "sit-down", Guzman said he was the world's leading supplier of heroin, methamphetamine, cocaine and marijuana.
White House chief of staff Denis McDonough told CNN: "One thing I will tell you is that this braggadocious action about how much heroin he sends around the world, including the United States, is maddening.
"We see a heroin epidemic, an opioid addiction epidemic, in this country... But El Chapo's behind bars - that's where he should stay."
The Mexican authorities would not say whether they would investigate Penn and a Mexican actress, Kate del Castillo, who apparently arranged the interview.
Mr McDonough declined to answer a question about whether the US would hand Penn over to Mexico for questioning.
"Well, it poses a lot of very interesting questions both for him and for others involved in this-so-called interview, so we'll see what happens on that - I'm not going to get ahead of it," he said.
Mr Rubio told ABC: "If one of these American actors who have benefited from the greatness of this country, who have made money from our free enterprise system, want to go fawn all over a criminal and a drug trafficker in their interviews, they have a constitutional right to do it. I find it grotesque."
February 2014: Recapture after 13 years on the run following "laundry basket" escape from Puente Grande maximum security prison
July 2015: Escape via tunnel from Altiplano prison
2 October 2015: Interviewed by US actor Sean Penn in Durango state jungle hideout and then by phone and video
17 October: Mexican officials announce narrow escape as police try to recapture him in neighbouring Sinaloa state; suffers face and leg injuries
January 2016: Recaptured in city of Los Mochis, Sinaloa state
Mexico has said it will begin the process of extraditing Guzman to the US, in line with extradition requests from 2015.
He is charged with smuggling vast amounts of drugs into the US.
No detail has been given about the timeframe for extradition but experts say the process could take months.
The BBC's Katy Watson, in Mexico City, says his extradition is by no means a foregone conclusion. The two countries have an extradition treaty but there are many steps that need to be taken and officials who need to approve the request.
Previous requests from the US have been turned down.
Guzman, who was named Public Enemy Number One by the Chicago Crime Commission in 2013, has been indicted by at least seven US federal district courts.
He was recaptured on Friday in the north-western city of Los Mochis in his home state of Sinaloa, which he had come to dominate through his drugs cartel.
During the raid, he managed to flee through a drain but was later caught by marines in a shootout.
Five drug gang suspects were killed in the operation and one marine wounded.