Cohen, who was sentenced to three years in prison on December 12, claimed at his hearing that he had "never asked for, nor would I accept, a pardon from President Trump".
Costello and Giuliani each told CNN that the emails, which have been turned over to Congress, did not have to do with pardons, but rather were meant to let Cohen know that Trump wasn't "mad at him".
Cohen's lawyer, Lanny Davis, and Trump lawyer Rudy Giuliani went back-and-forth in dueling interviews and tweets.More news: Trump blasts 'fake news' over Melania body double theory
Michael Monico told Rep. Elijah Cummings, D-Md., in the letter that Cohen had asked his lawyer to explore the possibility of a pardon before Cohen left a joint-defense agreement and turned against Trump last June.
In a statement to lawmakers on Tuesday, Cohen's legal team sought to clarify his recent testimony amid questions over whether Cohen sought, or Trump offered, a pardon to the man, who once declared he would take a bullet for the Republican president but has since flipped to cooperate with federal prosecutors.
'Bad lawyer and fraudster Michael Cohen said under sworn testimony that he never asked for a Pardon, ' Trump tweeted. He is going to jail for committing several crimes, including lying to Congress about the timeline of a Trump Organization effort to build a tower in Moscow, that he says were done to protect Trump.More news: Nancy Pelosi says impeaching Donald Trump 'just not worth it'
Trump tweeted last week that Michael Cohen "directly asked me for a pardon".
There is nothing inherently improper about a subject in a criminal investigation seeking a pardon from a president given the president's wide latitude in granting them.
But Cohen, in his closed-door congressional testimony, handed over the emails to back his claim that a pardon was dangled before he chose to cooperate with the feds, the network reported, citing sources. But investigators want to know if the prospects of presidential pardons were somehow offered or used inappropriately.More news: Brexit hangs in balance over tweaked deal
The House Oversight Committee chairman on Wednesday rejected Republican calls for a new investigation into President Trump's former personal lawyer Michael Cohen and whether he again lied to Congress. Cohen, in connection with a separate investigation, also pleaded guilty to tax and bank-related fraud charges and is expected to report to prison in May to serve a three-year sentence.
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