Acosta came under renewed scrutiny in recent days over his role years ago as a USA attorney in Miami, during which time he cut a secret non-prosecution agreement in 2008 with billionaire Jeffrey Epstein.
"Alex was a great Secretary of Labor and his service is truly appreciated", the president added, noting that Acosta would be replaced on an acting basis by the current deputy secretary, Pat Pizzella.
"We did what we did because we wanted to see Epstein go to jail", he said, refusing to apologize for his actions.More news: Simona Halep blitzes Serena Williams to win Wimbledon title
Given that background, UltraViolet's Thomas said, "Congress should open a full investigation into President Trump, who was directly implicated as an enabler of Epstein, and is self-confessed serial sexual predator with almost two dozen accusations against him".
Wallace said, "There were a lot of doubts about Alex Acosta already", particularly frustrations that he had been taking a more liberal stance in not pushing to deregulate rules in the workplace.
The arrest set in motion a chain of events that led to the resignation Friday of Labor Secretary Alex Acosta, who was the US attorney in Miami during the earlier investigation of Epstein.
"This double standard has no role in the Labor Department or any other part of our government", said CWA, "and we welcome his resignation".
Pressed on whether he had any regrets, 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.More news: Funeral held for ‘Dog the Bounty Hunter’ star Beth Champan
Mr Epstein, 66, was arrested on July 6 at Teterboro Airport in New Jersey, where he had returned on his private plane from Paris. "Today's world treats victims very, very differently", he said. Epstein had a social circle that over the years has included Trump, former President Bill Clinton and Britain's Prince Andrew.
"I was involved in thousands of cases, and not all of them turn out the way you think they should, but in that case it was very freakish".
Trump, who has previously described Epstein as a "terrific guy" who "likes attractive 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.
Seven months after James Mattis resigned as defence secretary, for example, there has yet to be confirmation hearings after Patrick Shanahan pulled out of the running.
Kirstjen Nielsen, outgoing secretary of Homeland Security, in April become the 15th cabinet official to depart in just over two years, a rate of turnover not matched in recent presidencies.
Nancy Pelosi, the Democratic speaker of the House of Representatives, and Democratic Senate Majority Leader Chuck Schumer had called on Tuesday for Acosta to resign.More news: National Football League suspends Jets’ Chris Herndon four games
Acosta took office as the nation's 27th labor secretary in early 2017, leading a sprawling agency that enforces more than 180 federal laws covering about 10 million employers and 125 million workers.
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