Speaking before reporters at the White House Friday, Acosta said it would be "selfish" for him to remain in the administration at this time.
They said the payment, along with $250,000 sent to another person who was a former employee and was named as a possible co-conspirator in the non-prosecution agreement, came after the Miami Herald last November began publishing a series of articles describing the circumstances of his state court conviction in Florida in 2008 and the deal to avoid federal prosecution.
According to an indictment, Mr Epstein arranged for girls under the age of 18 to perform nude "massages" and other sex acts for him in his NY and Florida homes, and paid some girls to recruit others, from at least 2002 to 2005.
Acosta would not say if he would make the same decision regarding Epstein now, considering the power of the #MeToo movement that led to the downfall of several powerful men publicly accused of sex crimes by women.
"I don't know whether he jumped or if he was pushed".
"I do not think it is right and fair to have Epstein as the focus rather than the incredible economy that we have today", the outgoing labour secretary said.
Residents of South Florida expressed relief that President Trump's Labor Secretary Alex Acosta is resigning his post.
On Wednesday, Alex Acosta gave a dispassionate, legalistic defence of his handling of the Jeffrey Epstein case, more than a decade ago. It wasn't enough to save his job. Given how quickly he departed after his performance, it wasn't even close.
Now the toxic swirl has claimed its first high-profile name.
"Mr. Acosta now joins the sprawling parade of President Trump's chosen advisors who have left the administration under clouds of scandal and corruption, leaving rudderless and discouraged agencies in their wake". He was arrested for trafficking underage girls earlier this week and will appear in court Monday. Former president Bill Clinton reportedly flew on Epstein's plane at least 26 times. "It's what I do".
Isidro "Sid" Garcia, another Palm Beach lawyer who is also representing an Epstein accuser told NPR it wasn't a bad idea for Acosta to go. "I threw him out of a club".
"This was him - not me", Trump said of the resignation decision.
"It shows you one thing".
"As part of the arrangement, Acosta agreed - despite a federal law to the contrary - that the deal would be kept from the victims".
"We did what we did because we wanted to see Epstein go to jail", said Acosta.
"That is why we intervened", he said.
While Acosta this week defended the deal, progressive groups did not let up in their criticism. Epstein would have faced a potential life sentence in prison.
"We now have 12 years of knowledge and hindsight and we live in a very different world". "Today's world treats victims very, very differently". Epstein agreed to plead guilty to state charges, register as a sex offender, and spend 13 months in county jail, during which time he was allowed to spend 12 hours a day, 6 days a week, out of the jail on "work release".
Acosta was confirmed in the Senate in early 2017 by a 60-38 vote, with all Republicans on board, along with eight Democrats and one independent. The heads of the Interior, Justice, State and Health departments have also either been fired or resigned, among other top staff during Trump tenure so far.