Epstein was accused of molesting dozens of girls in the early 2000s at his house in Florida and on the Caribbean island, but the charges were mostly dropped in a controversial plea deal reached by US attorneys in Florida working under Acosta in 2008.
Acosta said he wanted to avoid becoming a distraction and allow the administration to focus on the economy. "I will say this and I say it again loud and clear: Alex Acosta was a great secretary of labor".
By the "people" who were happy with that deal, Trump has to mean Jeffrey Epstein himself, because one giant reason Acosta is facing scrutiny is that, according to the findings of reporter Julie K. Brown, Acosta did not inform Epstein's victims of the deal he proposed to the defendant, despite his legal obligation to do so.
The centerpiece of Pizzella's work was organizing all-inclusive junkets for members of Congress and their wives, congressional staffers, and conservative influencers such as pollster Kellyanne Fitzpatrick-who now goes by her married name, Kellyanne Conway, and advises President Donald Trump-with first-class airfare and lodging at the beachfront Hyatt Regency on Saipan.
Trump, with Acosta at his side, said Friday he did not ask his secretary to leave and "I hate to see this happen".
But Trump did not originally want to be seen as cutting ties with him over a decade-old episode, even as some of his longest advisers believed Acosta's departure was inevitable given the cascade of sustained news coverage and the facts of the case. "I threw him out of a club".
Another court weighs fate of Obamacare
The outcome will apply to all states, but is expected to be appealed to the US Supreme Court . More than 800,000 Washingtonians depend on the ACA for their health care.
On Friday, Mr Trump reiterated "I'm not a fan of Jeffrey Epstein" after earlier saying they had a falling out "12 or 15 years ago" with him.
Top Democratic lawmakers and presidential candidates had demanded that Acosta resign. Epstein was arrested on July 6 on sex trafficking charges.
Earlier this week both Acosta and Trump sought to defend the plea deal.
Mr Acosta was the USA attorney in Miami when he oversaw a 2008 non-prosecution agreement with Epstein.
Mr Acosta did not apologise for his handling of the case, saying only that the deal - which closed the FBI investigation into whether there were more victims or perpetrators - was a guarantee of jail time. Some said the deal broke federal law because the victims were not told about the agreement.
"The rest of it, we'll have to look at it very carefully", Trump said in response to a question from a reporter in the Oval Office alongside Qatar's ruling emir Sheikh Tamim bin Hamad al-Thani.
Pressed on whether he had any regrets, Mr Acosta repeatedly suggested that circumstances had changed since then.
"The crimes committed by Epstein are horrific", Acosta tweeted. It turned out that the Acosta-engineered sweetheart deal gave him immunity from federal prosecution after a light sentence for crimes in Florida, but it did not give him immunity for his alleged exploitation of underaged girls in NY.