Senate Minority Leader Chuck Schumer, responding to Trump's statement last week that he would "100 percent" speak under oath about the Comey affair, said he would like the president to testify in public before the Senate.
Trump's assertion came after he branded Comey as a "leaker" and claimed "total and complete vindication" after ousted FBI director's testimony before a Senate Committee.
"I think we could work out a way it could be dignified, public, with questions, with Leader McConnell," Schumer told CBS News.
Trump's pledge to offer sworn testimony to Mueller came in a press conference the day after Comey's testimony before the Senate intelligence committee.
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The former FBI director detailed "disturbing" interactions with Trump that led to his firing on May 9.
Comey had last week said that he believed Trump asked him to end an investigation into former national security adviser Michael Flynn, which Trump has denied.
The president had said Comey's testimony vindicates his assertion that Trump himself was not personally under the investigation.
However, Trump and his attorney have disputed Comey's other assertions, including his claim that the president sought a pledge of loyalty.
Yesterday, Schumer also said he would like to clear up the matter of whether Trump does indeed have tapes of his conversations with Comey, as the president has suggested.
"Lordy, I hope there are tapes," Comey had said on Thursday.
"If there aren't tapes [Trump] should let that be known. No more game playing," Schumer said.