Sen. John Thune, the incoming Republican leader, is currently at Trump's Mar-a-Lago club for a meeting, sources familiar with the matter told ABC News.

The meeting comes as Thune is likely to face massive pressure from Trump and his Senate allies to push through all of Trump's nominees as quickly as possible.

Shortly after the news broke, Thune told ABC News he respected Gaetz's decision to withdraw from consideration for attorney general.

"That's obviously a decision he came to, and I think everybody had to make a decision that’s good for them and their family. And for whatever reason he decided not to pursue it," Thune said.

-ABC News' Katherine Faulders and Allison Pecorin

Trump has nominated Pam Bondi as his new pick for attorney general, after Matt Gaetz withdrew from consideration earlier Thursday.

Bondi is the former attorney general of Florida, serving from 2011 to 2019 and marking the first woman in that role.

"For too long, the partisan Department of Justice has been weaponized against me and other Republicans - Not anymore. Pam will refocus the DOJ to its intended purpose of fighting Crime, and Making America Safe Again," Trump said in a statement.

The position requires Senate confirmation.

Bondi has remained in Trump’s inner circle for years and has continued to advise him on legal matters. She was also one of the lawyers who defended Trump during his first Senate impeachment trial.

-ABC News' Lalee Ibssa and Katherine Faulders

House Ethics Committee Chairman Michael Guest of Mississippi told reporters that Matt Gaetz’s withdrawal from attorney general consideration "settles any involvement that the Ethics Committee should have in any matters involving Mr. Gaetz."

He added that the withdrawal "should end the discussion of whether or not the Ethics Committee should continue to move forward in this matter."

-ABC News' Lauren Peller

Senate Minority Leader Mitch McConnell, who earlier said he would not be the party’s Senate leader in the new Congress, announced Thursday he will be chairman of the Senate Rules Committee and the Defense Appropriations subcommittee when Republicans take control of the Senate in January.

Both positions are significant, given McConnell’s strained relationship with Trump.

The appointment to the Rules committee, which maintains the operating procedures of the Senate, is particularly interesting at a time when Trump has suggested he’s interested in pushing the boundaries of the Senate’s normal operating procedure.

In his statement, McConnell said, “Defending the Senate as an institution and protecting the right to political speech in our elections remain among my longest-standing priorities.”

McConnell could be instrumental in defense of the Senate filibuster or, potentially, recess appointments, which Trump has said he might use to circumvent Senate approval of some of his Cabinet picks, though party leadership still has the final say in these matters.

The appointment to lead the defense appropriations subcommittee is also significant for McConnell, who has said he sees advocating on behalf of U.S. self-defense and the defense of U.S. allies as a critical part of his role post-leadership. He could use the post to advocate for additional funding for Ukraine.

“America’s national security interests face the gravest array of threats since the Second World War. At this critical moment, a new Senate Republican majority has a responsibility to secure the future of U.S. leadership and primacy. I intend to play an active role in this urgent mission as Chairman of the Senate Appropriations Subcommittee on Defense, and I look forward to working closely with incoming Chair Susan Collins to accomplish our shared goal,” McConnell said in his statement.

-ABC News’ Allison Pecorin

Some of the Republican senators thought to be opposed to the selection of Matt Gaetz for attorney general because of obstacles to his confirmation openly praised his decision to step aside.

"I think that was an excellent move on behalf of the incoming President," Minority Leader Mitch McConnell said -- though it's not clear if Trump directed Gaetz to withdraw.

"I think it was a sound decision. I think it was important," said Sen. Lisa Murkowski, who had been among those publicly projecting serious concern about Gaetz's nomination.

Asked if she was relieved, Murkowski said, "I am. I think it was the right decision."

Sen. Mike Rounds, who had also expressed some concerns about Gaetz, said the move to withdraw was the "right decision to make."

"There was perhaps some information out there that the president was not aware of when he made the original recommendation. Part of this process is, the information comes out, and then at that point, as people re-evaluate or evaluate, you know, the president or the individual candidate may decide it's not the right time to pursue the nomination," Rounds said. "It may very well have been because of advice from the Senate rather than consent from the Senate."

Not all senators were as open on their views.

"That's obviously a decision he came to, and I think everybody had to make a decision that's good for them and their family. And for whatever reason he decided not to pursue it," Sen. John Thune, the incoming Republican leader, said.

When pressed on whether he felt it was the right choice, he said, "We respect his decision."

Many Republican senators said they were taken by surprise.

"I learned about it the same way everyone else did, by reading the announcement," Sen. Ted Cruz, who sits on the Senate Judiciary Committee and met with Gaetz on Wednesday, said.

-ABC News' Allison Pecorin