White House chief of staff Denis McDonough, appearing on Sunday television news shows, said he had read news accounts of Sean Penn's interview in Rolling Stone magazine with then-fugitive Joaquin "Chapo" Guzman before his recapture.
In the article, Guzman said he was the world's largest supplier of heroin, methamphetamine, cocaine and marijuana.
"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," McDonough said on CNN's State of the Union.
"We see a heroin epidemic, an opioid addiction epidemic, in this country," McDonough said.
"We're going to stay on top of this with our Mexican counterparts until we get that back in the box. But El Chapo's behind bars - that's where he should stay."
President Barack Obama plans to address the country's heroin epidemic in his State of the Union speech on Tuesday night, the White House has said.
Guzman, boss of the Sinaloa drug cartel, was arrested in Mexico on Friday morning and sent back to the prison he broke out of in July.
Mexican authorities said Penn's secret interview last year helped them catch the drug lord.
A Mexican government source has said authorities are considering whether to investigate Penn and a Mexican actress who helped him.
McDonough would not say 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 gonna get ahead of it," McDonough said.
Republican presidential candidate Marco Rubio, on ABC's This Week, had harsh words for Penn.
"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," Rubio said.
"(But) I find it grotesque."
