The administration's push to cast aside Berman set up an extraordinary political and constitutional clash between the Justice Department and one of the nation's top districts, which has tried major mob and terrorism cases over the years and is investigating Trump's personal lawyer, Rudy Giuliani.
It also comes as Trump seeks to purge officials perceived as not fully supporting him.
Barr had announced on Friday night that the USA attorney was stepping down and would be replaced by SEC chair Jay Clayton.
Mr Berman, US Attorney for the Southern District of NY, said the duke had "yet again sought to falsely portray himself to the public as eager and willing to co-operate with an ongoing federal criminal investigation into sex trafficking and related offences committed by Jeffrey Epstein and his associates, even though the prince has not given an interview to federal authorities, has repeatedly declined our request to schedule such an interview and almost four months ago informed us unequivocally - through the very same counsel who issued today's release - that he would not come in for such an interview".
In a letter made public by the Justice Department later Saturday, Barr said he expected to continue speaking with Berman about other possible positions within the department and was surprised by the statement he released.
While the Senate considers Clayton's nomination, Barr said, the job will be filled by Craig Carpenito, who now serves as the USA attorney in New Jersey. Hours later, the prosecutor issued a statement denying that he had resigned and saying that his office's "investigations would move forward without delay or interruption".
"POTUS, but not Barr, can remove him", Marty Lederman, a Georgetown University law professor, said in a social media statement.
Berman, he said, is welcome to testify at a committee hearing on the topic on Wednesday.
French Olympic hopeful climber Luce Douady, 16, dies after cliff fall
Bouldering is a form of rock climbing that does not use a rope or harness, and is performed on smaller rocks or artificial walls. FFME added that "the whole federation is in mourning", including Douady's "training comrades and coaches".
The Associated Press news agency, citing people familiar with the matter, said federal prosecutors in NY are investigating Giuliani's business dealings, including whether he failed to register as a foreign agent.
A spokesman for Gillibrand did not immediately respond to a request for comment.
House Judiciary Committee Chairman Jerry Nadler tweeted, "America is right to expect the worst of Bill Barr, who has repeatedly interfered in criminal investigations on Trump's behalf".
Berman was initially appointed to his position by Preet Bharara, who was also fired by Trump.
Geoffrey Berman has overseen prosecutions of associates of President Trump, including Trump's former personal attorney, Michael Cohen. On Saturday, a US judge denied the administration's request to block publication. Bharara, an outspoken critic of the president, said the timing of the push to replace his successor was unusual.
Other notable former Manhattan U.S. attorneys include Giuliani, Mary Jo White, who was the first and only woman to be the United States Attorney for the Southern District of NY and went on to beocme SEC Chair, former Director of the FBI James Comey, and Robert Morgenthau, who became the District Attorney of Manhattan and was the longest-serving district attorney in the history of the State of NY. Bharara wrote on Twitter, referring to the November 3 USA presidential election. "A previous action by this US attorney or one that is ongoing?"
Sources cite tension between Berman and Barr over the handling of a spate of cases, including the indictment of Turkish bank Halkbank.