Embattled Labor Secretary Alexander Acosta has announced he is resigning Friday morning. Acosta made the announcement himself, accompanying the president out of the White House residence before the president's departure for a trip to Milwaukee.

"As I look forward, I do not think it is right and fair for this administration's labor department to have (Jeffrey) Epstein as the focus rather than the incredibly economy we have today."

"I told [President Trump] the right thing was to step aside," he continued. "Cabinet positions are temporary trusts. It would be selfish to stay in this position and continue talking about a case that's 12 year old, rather than the amazing economy we have right now."

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Acosta had defended his handling of a decade-old plea deal with financier Jeffrey Epstein on sex crime charges when Acosta was the U.S. attorney in Florida's Southern District. Acosta faced renewed scrutiny over the case after Epstein was arrested on new federal sex trafficking charges in New York last week.

President Trump said that Acosta called him Friday morning and said it was entirely Acosta's decision.

U.S. President Donald Trump listens to Labor Secretary Alex Acosta talks to reporters as the president departs for travel to Milwaukee, Wisconsin from the South Lawn of the White House in Washington, U.S., July 12, 2019. Kevin Lamarque / REUTERS

Standing next to Acosta, Mr. Trump called him a "great labor secretary -- not a good one." He told reporters that Acosta "did a very good job...we're gonna miss him."

The president also defended Acosta's handling of the 2008 plea deal Acosta's office made with Epstein. Mr. Trump said people were initially happy with it, then changed their minds. Still, the president thought Acosta, in his press conference Wednesday, had ably defended the actions taken by federal prosecutors. The deal demanded Epstein register as a sex offender, pay restitution to the victims and serve 13 months in a county jail, though he was able to leave six days a week to work.

Acosta will leave the administration in seven days.

At a nearly hour-long press conference at the Labor Department on Wednesday, Acosta described Epstein's actions as "despicable," insisting Epstein might have gotten away without jail time if the U.S. attorney's office hadn't stepped in and taken over the case from the state of Florida. But Acosta struggled to answer questions about whether he would handle the case differently now, offering no apology to Epstein's victims.

Asked if he would make the same deal now, Acosta responded: "We live in a very different world. Today's world treats victims very, very differently," adding that "today, our judges do not allow victim-shaming by defense attorneys."

Acosta also faced criticism for keeping the federal deal not to prosecute Epstein a secret. In February, a federal judge said prosecutors had violated victims' rights by keeping the agreement secret. Acosta explained to reporters that prosecutors took this approach because the agreement negotiated with Epstein had "an unusual provision," in that it would require Epstein to pay victims restitution. He said that if the victims had been aware of the restitution negotiation and the deal fell apart, Epstein's attorneys could argue at trial that their testimony was compromised because they were going to be paid.

In his resignation letter to the president obtained by CBS News, Acosta called his role at the Labor Department "the honor of a lifetime."

"It has meant so much to me that you have offered your steadfast support in your private discussions and in your public remarks," Acosta wrote. "My resignation from this position will not diminish my support for you and your agenda. I believe you have done an incredible job and have the right vision for our nation by putting working American families at the center of your presidency."

Patrick Pizzella, deputy labor secretary, will take over as acting secretary.