It isn't every day that a comedian manages to speak to the president of the United States by pretending to be a U.S. senator, but "Stuttering John" podcaster John Melendez claims he did that this week. Now, Melendez said Sunday evening, the United States Secret Service wants to interview him. And to represent him, Melendez has enlisted Michael Avenatti, the attorney for adult film actress Stormy Daniels in her lawsuit against President Trump.

The Secret Service did not respond to a request from CBS News to confirm the meeting. Avenatti confirmed to CBS News' Paula Reid that he is representing Melendez.

As for the interview with the Secret Service, Melendez had said earlier that it was set for Monday morning at his home in California. But now Avenatti wants to review the facts before the interview takes place.

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A former Secret Service agent told CBS News that the agency likely wouldn't be investigating how the call happened — it would potentially be investigating if Melendez posed a threat.

The White House has not acknowledged the prank call, earlier saying, "we are not engaging on this at all."

But the White House did reach out to Sen. Bob Menendez's office Thursday morning to inform the New Jersey Democrat about the incident, according to a source familiar with the call.

So, how did a comedian apparently reach the U.S. president?

Melendez told CBS News on Saturday that he and his producer were doing his "Stuttering John" podcast when they decided to call the White House. At first, according to Melendez's account, he called in as himself. He said he thought he could get through, given that he has known Mr. Trump for many years. But the White House didn't patch him through.

Melendez said he then called back again, claiming to be the senator's assistant, using what he described as a bad British accent.

That apparently worked. The White House, Melendez said, took the call, and called him back on his cell. When he was asked why his number included an area code from California, Melendez claimed to be on holiday.

"How dumb are you to think that the area code changes when you go to a different city?" Melendez said to CBS News.

Melendez said that Mr. Trump's son-in-law and senior adviser Jared Kushner then called him from Air Force One. Kushner asked what he wanted to discuss with the president, according to Melendez, and Melendez told Kushner he had an extensive conversation with Mr. Trump on immigration, and wanted to continue the conversation.

Melendez claimed he got a call back within 20 minutes, patching him through to Mr. Trump aboard Air Force One.

In the conversation, a voice that Melendez claimed is Mr. Trump's congratulated the comedian on his success, believing him to be the senator (the Justice Department in January declined to re-try the Democratic senator's public corruption case). The two then discussed immigration and Mr. Trump's future Supreme Court pick.

Melendez said that when he arrived home, neighborhood kids told him the Secret Service had been banging on his door. The children claimed, according to Melendez, that Secret Service agents showed their badges.

On Sunday morning, Melendez told CBS News he was hopeful that he wouldn't face any punishment. "I don't think the Secret Service is going to do anything, because I didn't make any money off of this, so hopefully they're going to let it go," he said.

But Sunday evening, Melendez said that the Secret Service did reach him by phone to schedule an interview. "Are you going to arrest me?" Melendez said he asked the agent. The response: "We want to interview you."

As for the prank, Melendez told CBS News that all the White House needed to do was ask his party affiliation and state to stump him; Melendez said he only knows the senator's name. "That's gotta scare most Americans, that's how easy you can infiltrate this administration," he said.