President Donald Trump says Labour Secretary Alexander Acosta is stepping down from his role.

The move comes following criticism of his handling of a plea deal with wealthy financier Jeffrey Epstein, who is accused of sexually abusing dozens of underage girls.

Jeffrey Epstein, centre, appears in court in West Palm Beach (Uma Sanghvi/Palm Beach Post via AP)

President Trump, with Mr Acosta at his side, made the announcement as he left the White House for a trip to Wisconsin and Ohio.

The president said Mr Acosta had been a “great” labour secretary.

“I hate to see this happen,” President Trump said. He said he did not ask Mr Acosta to leave the Cabinet.

Mr Acosta said his resignation would be effective in seven days.

He said he did not think it was right for his handling of Epstein’s case to distract from his work as secretary of labour.

“My point here today is we have an amazing economy and the focus needs to be on the economy job creation,” Mr Acosta said.

Mr Acosta was the US attorney in Miami when he oversaw a 2008 non-prosecution agreement with Epstein.

Epstein avoided federal charges, pleaded guilty to state charges and served 13 months in jail.

Similar charges recently filed against Epstein by federal prosecutors in New York had put Mr Acosta’s role in the 2008 deal under renewed scrutiny.

Top Democratic politicians and presidential candidates had demanded that Mr Acosta resign over his handling of the agreement, which a federal judge has said violated federal law because Mr Acosta did not notify Epstein’s victims of the arrangement.

The Justice Department has been investigating.

President Trump had initially defended Mr Acosta, but said he would look “very closely” his handling of the 2008 agreement.

The deal came under scrutiny earlier this year following reporting by the Miami Herald.

Epstein, 66, reached the deal to secretly end a federal sex abuse investigation involving at least 40 teenage girls that could have landed him behind bars for life.

He instead pleaded guilty to state charges, spent 13 months in jail, paid settlements to victims and is a registered sex offender.

Mr Acosta had attempted to clear his name, and held a news conference — encouraged by President Trump — to defend his actions.

In a 50-plus-minute rebuttal, Mr Acosta argued his office had secured the best deal it could at the time and was working in the victims’ best interests.

“We did what we did because we wanted to see Epstein go to jail,” he said, refusing to apologise for his actions.

“We believe that we proceeded appropriately.”

Pressed on whether he had any regrets, Mr Acosta repeatedly suggested that circumstances had changed since then.

“We now have 12 years of knowledge and hindsight and we live in a very different world,” he said.

“Today’s world treats victims very, very differently.”