It also comes as Trump seeks to purge officials perceived as not fully supporting him.
Berman has also overseen the prosecution of two Florida businessmen, Lev Parnas and Igor Fruman, who were associates of Giuliani and tied to the Ukraine impeachment investigation.
However, that apparently came as news to Berman, who stated that he only found out about the development through the attorney general's press release.
"I will step down when a presidentially appointed nominee is confirmed by the Senate", the attorney said.
"Until then, our investigations will move forward without delay or interruption", he continued.
While Berman is pushing back against leaving his post, Attorney General Barr's press release indicated that President Trump has already appointed an interim replacement for Berman. "We welcome Mr. Berman's testimony and will invite him to testify".
In a statement, Graham said Clayton's nomination would still be required to go through the usual practice of getting approvals from his home-state senators, in this case Democrats Chuck Schumer and Kirsten Gillibrand of NY. "As chairman, I have honored that policy and will continue to do so".
He was responding to the statement from the duke's legal team, who earlier this month issued a strongly-worded defence of their client saying he had made three offers to give a witness statement.
Chad Daybell charged after authorities searched his home, found humans remains
Initially, the death was ruled as natural but it is now considered suspicious and her remains have been exhumed for an autopsy. Lori's brother claimed that the shooting was in self-defense and no charges were brought against him.
A spokesman for Gillibrand did not immediately respond to a request for comment.
Last fall, Justice Department officials discussed replacing Berman with Ed O'Callaghan, a senior official, but then prosecutors indicted the Giuliani associates, a move that appeared to extend Berman's tenure.
Why it matters: Berman oversaw one of the highest profile districts in the country and many politically charged prosecutors, including those over President Trump's former attorney Michael Cohen and investigations into hush money payments during the 2016 election.
Berman also headed the prosecution of Michael Cohen, Trump's former lawyer.
Any forced ouster of Berman is likely to draw scrutiny inside the United States attorney's office and among career prosecutors. Bharara, an outspoken critic of the president, said the timing of the push to replace his successor was unusual.
The U.S. Attorney for the Southern District of NY is in a fight with the Justice Department over his job. Mr Bharara wrote on Twitter, referring to the upcoming United States presidential election in November. But as USA attorney for the Southern District of NY, he won over some sceptics after he went after Trump allies.
But it's quite likely that Berman is wrong and Barr right about the President's power to fire a US Attorney. The judges were legally obligated to fill the position because Trump left it vacant without a Senate-confirmed attorney for more than one year. Carpenito, Vladeck wrote on Twitter, is neither of those. The episode occurred months after Berman assumed the role of USA attorney.
Clayton was previously a corporate lawyer at Sullivan & Cromwell, and would be the first non-prosecutor in the post if confirmed.