US President Donald Trump told reporters that he and Mr Acosta spoke on the phone earlier on Friday and that it was Mr Acosta's decision to step down.
As the then US Attorney in Miami, Acosta oversaw the non-prosecution deal handed to Epstein. Acosta said he didn't think it was right for his handling of Epstein's case to distract from his work as secretary of labour.
"At the end of the day, based on the evidence, professionals within a prosecutor's office decided that a plea that guarantees someone goes to jail, that guarantees he register [as a sex offender] generally and guarantees other outcomes is a good thing, '" Acosta said at the time. "Not just him. I can only say this from what I know and what I do know is that he's been a great - really great secretary of labor".
Democrats had called for him to quit over his handling of the Epstein case.
"He traveled on Epstein's jet at least once", O'Brien continued, adding, "I spent about two years, a lot of time with Trump in the mid-2000s, and he routinely talked about Jeffrey Epstein as someone he admired, he felt they were in sync".
However, Mr Trump has said the pair fell out "12 or 15 years ago" and reiterated on Friday that he was "not a fan of Jeffrey Epstein".
In 2015, Epstein's address book was published online by news outlet Gawker, which obtained the book following its appearance in court proceedings after Epstein's former house manager tried to sell it in 2009. Epstein had a social circle that over the years has included Trump, former President Bill Clinton and Britain's Prince Andrew. He faces federal charges of sex trafficking and sex trafficking conspiracy.
Trump said Friday that deputy Pat Pizzella will took over as acting labour secretary, one of a host of positions now vacant or with officials serving in an acting capacity.
The arrest set in motion a chain of events that led to the resignation Friday of Labor Secretary Alex Acosta, who was the USA attorney in Miami during the earlier investigation of Epstein.
The deal came under scrutiny earlier this year following reporting by the Miami Herald, and Democrats en masse had called for Acosta's resignation.
Acosta said his resignation would be effective in seven days.
Trump, who has previously described Epstein as a "terrific guy" who "likes lovely women", also attempted to distance himself from the financier, saying he was "not a fan" and that the two had a "falling out" years ago. Acosta said Epstein would have had an even lighter sentence if not for the deal. The letter also said that since the indictment was unsealed on Monday, "several" more women have come forward alleging that they were victims of Epstein when they were minors.
Top Democratic lawmakers and presidential candidates had demanded that Acosta resign.
"It is the job of the Labor Department to enforce laws that protect all workers", the union said in a statement. The Justice Department has been investigating.
Trump puts social media on notice after summit
CNN's complaints had already resulted in the White House disinviting Ben Garrison , a web cartoonist and Trump supporter. Kamala Harris by saying she is not an "American black" following the first Democratic presidential debates.
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