Michael Cohen, former attorney to President Donald Trump testifies before the House Oversight Committee at the Rayburn House Office Building on Wednesday February 27, 2019 in Washington, DC.

President Donald Trump on Friday claimed that his former personal lawyer and fixer Michael Cohen last year "directly asked me for a pardon."

But Cohen, who recently testified that he had "never" sought a pardon from Trump, said that the president's claim was "just another set of lies."

The exchange was the latest back-and-forth between the Trump and Cohen camps over the question of if and when Cohen had actively sought a presidential pardon for the crimes he admitted to last year.

"Bad lawyer and fraudster Michael Cohen said under sworn testimony that he never asked for a Pardon. His lawyers totally contradicted him," Trump tweeted, referencing Cohen's testimony last week claiming he had not and would not seek a pardon from his ex-boss for his crimes.

"He lied! Additionally, he directly asked me for a pardon. I said NO. He lied again! He also badly wanted to work at the White House. He lied!"

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Trump had teased his new claim about an hour earlier when he spoke to reporters on the South Lawn of the White House.

"His [Cohen's] lawyer said that they went to my lawyers and asked for pardons," Trump said. "And I can go a step above that but I won't go to it now."

A half-hour after Trump's tweet, Cohen responded on Twitter.

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Cohen's legal advisor Lanny Davis had no immediate comment on the president's allegation.

The White House had no immediate comment.

Last week, Cohen testified at length under oath before the House Oversight and Government Reform Committee about Trump.

"I have never asked for, nor would I accept, a pardon from President Trump," Cohen told the committee.

The 52-year-old disbarred lawyer is due to begin a three-year prison term in May for multiple crimes, some of which relate to his work for Trump.

Cohen, as part of his guilty plea, said Trump directed him to facilitate the payments of hush money to porn star Stormy Daniels and Playboy model Karen McDougal shortly before the 2016 presidential election to keep them both quiet about their alleged affairs with Trump. Cohen also pleaded guilty to having lied to Congress about details of an aborted plan to build a Trump Tower in Moscow.

Trump has denied any wrongdoing and denies having had sex with either Daniels or McDougal.

On Wednesday, The Wall Street Journal reported that Cohen in the spring of 2018 told his lawyer at the time to ask about the possibility of a pardon from Trump, several weeks after the FBI raided his Manhattan home, office and the hotel room where he has been living with his family during ongoing home renovations.

Davis on Thursday said in a statement that before Cohen decided last year to leave a joint defense agreement with Trump's lawyers, "Michael was open to the ongoing 'dangling' of a possible pardon by Trump representatives privately and in the media."

"During that time period, he directed his attorney to explore possibilities of a pardon at one point with Trump lawyer Rudy Giuliani as well as other lawyers advising President Trump," Davis said.

"But after July 2, 2018, Mr. Cohen authorized me as a new lawyer to say publicly Mr. Cohen would never accept a pardon from President Trump even if offered. That continues to be the case. And his statement at the Oversight Hearing was true — and consistent with his post joint defense agreement commitment to tell the truth."

House Oversight Chairman Elijah Cummings, D-Md., said Thursday that he planned to look into Cohen's testimony about the issue of a pardon given the Journal story and the comments by Davis since last week. Cummings noted that he had warned Cohen about the need to be truthful in his testimony.

"I told him, 'I will nail you to the cross [if you lie].' And I meant that," Cummings said Thursday. "I gotta make sure they are true inconsistencies and not outright lies. And then I gotta find out if it meets even the threshold that the [Department of Justice] would even want to look at it."

Trump has hinted that he would be open to pardoning some of his associates who, like Cohen, have been investigated in special counsel Robert Mueller's probe of Russian election interference and possible collusion with Trump's presidential campaign in 2016.

In November, Trump said a pardon was "not off the table" when asked about his former campaign chairman Paul Manafort, who was convicted on bank and tax fraud charges and later pleaded guilty to other crimes in cases lodged by Mueller.

Trump denied at the time that a pardon for Manafort had ever been discussed. Manafort's spokesman has declined inquiries about whether the ex-campaign chief sought a pardon.