The interview was conducted in October in the Mexican jungle after El Chapo Guzman’s jail break, and published by Rolling Stone magazine.
A White House spokesman said Sean Penn’s “so-called interview” was “maddening”, while Marco Rubio said it was “grotesque”.
El Chapo (Shorty) Guzman, 58, was recaptured on January 8 after months on the run.
Unnamed Mexican officials say Sean Penn’s secret meeting helped lead them to the boss of the Sinaloa drug cartel.
El Chapo Guzman has now been returned to the maximum-security Altiplano jail, from where he escaped in July 2015 via a tunnel dug to the shower in his cell.
In the Rolling Stone article, the result of a seven-hour “sit-down”, El Chapo 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 Sean Penn and a Mexican actress, Kate del Castillo, who apparently arranged the interview.
Denis McDonough declined to answer a question about whether the US would hand Sean 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.
Marco 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.”
Mexico has said it will begin the process of extraditing El Chapo 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.
Mexico and the US 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.
El Chapo 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.
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