"It poses a lot of very interesting questions, both for him and for others involved in this … so-called interview," McDonough told Jake Tapper on CNN's State of the Union on Sunday.
"And one thing I will tell you is that this braggadocio's action about how much heroin he sends around the world, including to the United States, is maddening," McDonough said of Guzman. "We see a heroin epidemic, opioid addiction epidemic in this country. So, we're going to stay on top of this, with our Mexican counterparts, until we get that back in the box."
In the interview, Guzman's first in years, he admitted to operating a drug empire. Penn has faced backlash for his role in the case and is reportedly under investigation by the Mexican government, according to ABC News. But authorities also told the Associated Press the clandestine meeting helped them first locate the drug kingpin.
Penn broke his silence on the controversial interview in a brief email statement to the Associated Press on Monday, writing simply, "I've got nothin' to hide."
White House press secretary Josh Earnest discussed the Rolling Stone interview with reporters during a press briefing on Monday, saying he did not know whether the Mexican government would be investigating Penn. When asked if President Obama had read the interview, Earnest said he had not spoken with the president about it.
"The capture of Mr. Guzman has been a high priority both for Mexico and the United States. Mexican authorities have been aggressive about looking for Mr. Guzman and bringing him into custody," Earnest said. "We obviously commend the Mexican authorities for their success and … we're going to continue to work with Mexico and other partners around the world to respond to the threats that are posed by transnational criminal organizations."
Earnest added that he could not get into the specifics of Guzman's case but said he is facing "serious charges" in the U.S. and the standard procedure would be for the drug kingpin to be extradited to the U.S. CNN reported Saturday that Mexico will begin proceedings for the extradition but the process could take months.
In another appearance on ABC's This Week, McDonough said he was "appalled" by Guzman's comments to Penn. He was not alone. Florida Sen. Marco Rubio called the interview "grotesque."
"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," Rubio said on This Week.
"Sean Penn is not someone I spend a lot of time thinking about," the GOP hopeful added. "I didn't even know he was still around. I think he made movies a long time ago or something."
The two-time Oscar winner secretly met with Guzman while he was on the run from authorities following an escape from a Mexican prison last year. During their sitdown in October, which began with a "compadre hug" and lasted seven hours, Guzman boasted to Penn that he "supplies more heroin, methamphetamine, cocaine and marijuana than anybody else in the world" – but said he did not consider himself a violent person. "Look, all I do is defend myself, nothing more. But do I start trouble? Never," he said.
Republican presidential front-runner Donald Trump, for whom Guzman allegedly issued a $100 million bounty last year, also came up in the Rolling Stone interview published on Saturday.
When Penn mentioned Trump's name, Guzman smiled and said, "Ah! Mi amigo!"