WASHINGTON (CBSNewYork/CBS News/AP) — President Donald Trump said Saturday that “we can make a fast decision” on a new FBI director, possibly by late next week, before he leaves on his first foreign trip since taking office.

“Even that is possible,” he told reporters when asked whether he could announce his nominee by Friday, when he is scheduled to leave for the Mideast and Europe.

Four candidates to be the bureau’s director were in line Saturday for the first interviews with Attorney General Jeff Sessions and his deputy, Rod Rosenstein, at Justice Department headquarters. They are among nearly a dozen candidates Trump is considering, a group that includes several lawmakers, attorneys and law enforcement officials.

More: President Trump Delivers Commencement Address At Liberty University

“I think the process is going to go quickly. Almost all of them are very well known,” Trump said while flying to Lynchburg, Virginia, where he was giving the commencement address at Liberty University. “They’ve been vetted over their lifetime essentially, but very well known, highly respected, really talented people. And that’s what we want for the FBI.”

The Trump administration is looking to fill the job, which requires Senate confirmation, after Trump abruptly fired Director James Comey on Tuesday.

The White House said in a statement that Comey was terminated and removed from office based on “the clear recommendations of both Deputy Attorney General Rod Rosenstein and Attorney General Jeff Sessions.”

“The FBI is one of our Nation’s most cherished and respected institutions and today will mark a new beginning for our crown jewel of law enforcement,” President Trump said in a statement.

Trump’s letter directly to Comey was also released Tuesday afternoon. Trump said in the letter that he had agreed with Sessions and Rosenstein’s recommendations and “you are hereby terminated and removed from office, effective immediately.”

During an interview Saturday night on Fox News, the president said he wants to do away with the traditional daily White House press briefings.

“Let’s not ever do anymore press briefings,” he said.

Trump said he may hold his own briefings every two weeks instead and hinted a major shakeup could be coming to his press team, including embattled White House Press Secretary Sean Spicer, CBS2’s Brian Conybeare reported.

Trump: “He’s a wonderful human being. He’s a nice man.”

Jeanine Pirro: “Is he your press secretary today and tomorrow? Will he be tomorrow?”

Trump: “He’s doing a good job, but he gets beat up.”

The president admitted his press team has trouble keeping up with him and his tweets.

Former Bush defense secretary Robert Gates told John Dickerson on ‘Face The Nation’ that Comey’s firing was “not terribly well done.” He said the Trump administration could have done a much better job explaining Comey’s dismissal instead of the conflicting stories that came out of the White House.

“Having a single story in line in terms of how it happened and why it happened, that everybody is on the same page, and then what the next steps are I think helps to diminish the blowback that you get,” Gates said.

The first candidate to arrive was Alice Fisher, a high-ranking Justice Department official in the George W. Bush administration. She left after about an hour and a half inside the building and declined to comment to reporters.

Among those also expected to be coming were acting FBI director Andrew McCabe, Michael J. Garcia, a former U.S. attorney in Manhattan who now sits on New York’s highest court, GOP Sen. John Cornyn of Texas, the No. 2 Senate leader and a former state attorney general, and CBS News national security analyst Fran Townsend, Conybeare reported. Former NYPD Commissioner Ray Kelly has also been mentioned.

Fisher formerly served as assistant attorney general for the Justice Department’s Criminal Division. She faced resistance from Democrats during her confirmation over her alleged participation in discussions about detention policies at the Guantanamo Bay facility in Cuba. She also was deputy special counsel to the Senate special committee that investigated President Bill Clinton’s Whitewater scandal.

The FBI has never had a female director.

(© Copyright 2017 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)

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