By Melissa Fares and Nate Raymond

NEW YORK (Reuters) - Preet Bharara, the top federal prosecutor in Manhattan known for pursuing a series of cases targeting public corruption and crime on Wall Street, said on Wednesday he has agreed to remain in his post after Donald Trump becomes U.S. president.

Bharara, appointed to his position by Democratic President Barack Obama in 2009, told reporters following a meeting with the Republican president-elect at Trump Tower in Manhattan that Trump asked him to stay on during his administration and he accepted. Trump takes office on Jan. 20.

"We had a good meeting," Bharara said. "I said I would absolutely consider staying on. I agreed to stay on."

The announcement's timing, when Trump has not yet finished filling all Cabinet-level positions, was unusual. But some former prosecutors who served under Bharara said they were not surprised their former boss would be willing to remain as the U.S. Attorney for the Southern District of New York.

"I think Preet is an independent, law enforcement-minded prosecutor who loves his job and is clearly talented in it," said Arlo Devlin-Brown, a former chief of Bharara's public corruption unit who is now a partner at the law firm Covington & Burling.

U.S. Senator Charles Schumer of New York, the incoming Senate Democratic leader who Bharara previously worked for as chief counsel, said Trump called him last week to ask what he thought about Bharara staying in his job.

"I am glad they met and am glad Preet is staying on," Schumer said in a statement. "He's been one of the best U.S. Attorneys New York has ever seen."

CORRUPTION, INSIDER TRADING

Bharara's office has pursued an aggressive push against corruption in state and city politics, an agenda that could fit with Trump's vow to "drain the swamp" in Washington.

Those political investigations led last year to the convictions of former New York Assembly Speaker Sheldon Silver, a Democrat, and former New York Senate Majority Leader Dean Skelos, a Republican, in separate corruption trials.

Bharara also brought dozens of successful cases against insider traders and was on the cover of Time magazine in 2012 with the headline "This man is busting Wall St."

Those cases include the 2011 conviction of Galleon Group founder Raj Rajaratnam, who is serving an 11-year prison term, and a $1.8 billion settlement and plea deal in 2013 with hedge fund SAC Capital Advisors LP.

His 227-lawyer office also secured corporate settlements with companies including General Motors Co and JPMorgan Chase & Co; won several convictions and guilty pleas of former employees of Ponzi scheme operator Bernard Madoff; and prosecuted Suleiman Abu Ghaith, a son-in-law of the late al Qaeda leader Osama bin Laden.

Bharara's office's priorities have often matched those set by Obama's Justice Department.

Amid an increase in civil rights investigations nationally, for example, Bharara's office joined a lawsuit that led to a settlement in 2015 aimed at reducing violence in New York City's Rikers Island jail complex.

How priorities set by the Justice Department under Trump's pick for attorney general, Republican Senator Jeff Sessions of Alabama, affects the cases Bharara's office pursues remains unclear.

"Obviously there is likely be some changes in priorities from Main Justice (the department's Washington headquarters), and the office will have to adjust to those," said Richard Zabel, who previously served as Bharara's deputy before becoming hedge fund Elliott Management's general counsel.

Bharara said his office had for the past seven years pursued its work "independently, without fear or favor." Former prosecutors they expect that to stay the same.

"He would have only taken it on if he were 100 percent confident that that independence could be preserved," said Matthew Schwartz, partner at the law firm Boies, Schiller & Flexner and a former prosecutor under Bharara.

(Reporting by Melissa Fares and Nate Raymond; Additional reporting by Nathan Layne; Editing by Bill Trott and Will Dunham)