He faced heavy fire from both sides of the aisle during congressional testimony about his inquiry on Tuesday.
Republicans demanded to know why Mr Hur, 51, had decided not to prosecute the president.
Democrats attacked Mr Hur’s remarks in his explosive report on Mr Biden’s mental acuity.
During a tumultuous stint as a top aide to the deputy US attorney general under former President Donald Trump, Mr Hur was known for his unflappable demeanor.
In an interview with the New York Times, Mr Rosenstein said the department had found itself under a partisan microscope during that tenure.
Mr Rosenstein said he was at risk of being fired by Mr. Trump because of his choice to appoint special counsel Robert Mueller to investigate Mr Trump’s alleged ties to Russia.
“We were coming under tremendous criticism from the commentators – and the president – and Rob kept his head down, pushed ahead, and never lost his sense of humor,” Mr Rosenstein said of Mr Hur.
Over more than a decade as a federal prosecutor, Mr Hur has worked on cases involving national security, violent crime, and public corruption.
He clerked for the late William Rehnquist, a conservative chief justice of the US Supreme Court who was originally appointed by Richard Nixon.
Mr Hur was an aide at the Justice Department to Christopher Wray before Mr Wray was appointed in 2017 to head the FBI.
The son of Korean immigrants, Mr Hur graduated from Harvard College and Stanford Law School.
He met his future wife, then-law student Cara Brewer, in 2002 on the Washington DC subway as she pored over some legal notes, and invited her out for dinner on the spot. They wed two years later.
Mr Hur was appointed in 2017 by President Trump as the chief federal law enforcement officer in Maryland.
In that role, he handled several high-profile cases, including tax evasion charges against former Baltimore Mayor Catherine Pugh, a Democrat.
Mr Hur departed from that position when Mr Trump left office in 2021.
Despite his work in the Republican administration, Mr Hur drew praise at the time from Democrats.
As he left the federal government three years ago, Maryland’s two senators, Chris Van Hollen and Ben Cardin praised Mr Hur’s “excellent service” in having “faithfully followed the facts and the law”.
Yet Mr Hur has found himself in a political maelstrom since he released a 345-page report in February that alleged Mr Biden had “wilfully retained and disclosed classified materials”, but should not face criminal charges.
Investigators interviewed 147 witnesses, including Mr. Biden himself, whom Mr. Hur said seemed to be a “sympathetic, well-meaning, elderly man with a poor memory”.
Mr Hur has maintained his composure as he faces potshots from left and right. But his unruffled approach will be no surprise to at least one colleague.
Mr Hur has most recently been in private practice as a partner at the Washington DC office of Gibson, Dunn & Crutcher.
Thomas Dupree, who worked alongside Mr. Hur at the law firm, described him as “a very talented lawyer, a man of excellent judgment and a man of the highest integrity”.
