WASHINGTON — President Donald Trump said Monday he wants the FBI to do a “comprehensive” investigation into allegations of sexual misconduct by Brett Kavanaugh. But he also said he stands by his Supreme Court nominee “all the way.”

Trump said during a Rose Garden press conference that he wants the probe to wrap up quickly because the accusations have been “so unfair” to Kavanaugh and his family. But he said it’s fine with him if the FBI wants to pursue accusations made by three women who have publicly come forward even as he has left the scope of the investigation to Senate Republicans.

“My White House will do whatever the senators want,” Trump said. “The one thing I want is speed.”

The president added, “We don’t want to go on a witch hunt, do we?”

Trump also said he was surprised Kavanaugh has been so open about his beer drinking, one area Democrats are planning to focus on as they question whether the nominee was fully truthful in his testimony before the Senate.

FBI agents interviewed one of the three women who have accused Kavanaugh of sexual misconduct as Republicans and Democrats quarreled over whether the bureau would have enough time and freedom to conduct a thorough investigation before a high-stakes vote on his nomination to the nation’s highest court.

The White House insisted it was not “micromanaging” the new one-week review of Kavanaugh’s background, but some Democratic lawmakers claimed the White House was keeping investigators from interviewing certain witnesses. Trump tweeted that no matter how much time and discretion the FBI was given, “it will never be enough” for Democrats trying to keep Kavanaugh off the bench.

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Even as the FBI explored the past allegations that have surfaced against Kavanaugh, another Yale University classmate came forward to accuse the federal appellate judge of being untruthful in his testimony to the Senate Judiciary Committee about the extent of his drinking in college.

As the fresh review unfolded, the prosecutor who was brought in by Republicans to handle questioning at last week’s hearing outlined in a new memo why she did not believe criminal charges would be brought against Kavanaugh if it were a criminal case rather than a Supreme Court confirmation process. Rachel Mitchell wrote that she did not believe a “reasonable prosecutor would bring this case based on the evidence before the Committee.”

Mitchell argued that that there were inconsistencies in accuser Christine Blasey Ford’s narrative and said no one has corroborated Ford’s account. Ford, a California college professor, was not questioned as part of a criminal proceeding but in the confirmation process.

In speaking to FBI agents, Deborah Ramirez detailed her allegation that Kavanaugh exposed himself to her at a party in the early 1980s when they were students at Yale University, according to a person familiar with the matter who was not authorized to publicly discuss details of a confidential investigation.

Kavanaugh has denied Ramirez’s allegation.

The person familiar with Ramirez’s questioning, who spoke to The Associated Press on condition of anonymity, said she also provided investigators with the names of others who she said could corroborate her account.

But Ford, who says Kavanaugh sexually assaulted her when they were teenagers, has not been contacted by the FBI since Trump on Friday ordered the agency to take another look at the nominee’s background, according to a member of Ford’s team.

Kavanaugh has denied assaulting Ford.

In a statement released Sunday, a Yale classmate of Kavanaugh’s said he is “deeply troubled by what has been a blatant mischaracterization by Brett himself of his drinking at Yale.” Charles “Chad” Ludington, who now teaches at North Carolina State University, said he was a friend of Kavanaugh’s at Yale and that Kavanaugh was “a frequent drinker, and a heavy drinker.”

“On many occasions I heard Brett slur his words and saw him staggering from alcohol consumption, not all of which was beer. When Brett got drunk, he was often belligerent and aggressive,” Ludington said. While saying that youthful drinking should not condemn a person for life, Ludington said he was concerned about Kavanaugh’s statements under oath before the Senate Judiciary Committee.

Speaking to the issue of the scope of the FBI’s investigation, White House press secretary Sarah Huckabee Sanders said White House counsel Don McGahn, who is managing Kavanaugh’s nomination, “has allowed the Senate to dictate what these terms look like, and what the scope of the investigation is.”

White House counselor Kellyanne Conway said the investigation will be “limited in scope” and “will not be a fishing expedition. The FBI is not tasked to do that.”

Senate Judiciary Committee member Jeff Flake, R-Ariz., requested an investigation last Friday — after he and other Republicans on the panel voted along strict party lines in favor of Kavanaugh’s confirmation — as a condition for his own subsequent vote to put Kavanaugh on the Supreme Court.

Another committee member, Sen. Lindsey Graham, R-S.C., said Sunday that testimony would be taken from Ramirez and Kavanaugh’s high school friend Mark Judge, who has been named by two of three women accusing Kavanaugh of sexual misconduct.

“I think that will be the scope of it. And that should be the scope of it,” Graham said.

Sen. Dianne Feinstein of California, the top Democrat on the Judiciary Committee, called on the White House and the FBI to provide the written directive regarding the investigation’s scope. In a letter Sunday, she also asked for updates on any expansion of the original directive.

Sen. Susan Collins said Sunday she is confident in the investigation and “that the FBI will follow up on any leads that result from the interviews.” The Maine Republican supports the new FBI investigation and is among a few Republican and Democratic senators who have not announced a position on Kavanaugh.

Republicans have 51 seats in the closely divided 100-member Senate and cannot afford to lose more than one vote on confirmation.

Senate Republicans discussed the contours of the investigation with the White House late Friday, according to a person familiar with the call who was not authorized to discuss it publicly.

Senate Majority Leader Mitch McConnell, R-Ky., had gathered Judiciary Committee Republicans in his office earlier. At that time, the scope of the investigation was requested by Flake, Collins and Sen. Lisa Murkowski of Alaska, said McConnell’s spokesman Don Stewart.

Murkowski is not on the committee, but also has not announced how she will vote on Kavanaugh’s confirmation.

Sanders said Trump, who has vigorously defended Kavanaugh but also raised the slight possibility of withdrawing the nomination should damaging information be found, “will listen to the facts.”

At least three women have accused Kavanaugh of years-ago misconduct. He denies all the claims.

The third woman, Julie Swetnick, accused Kavanaugh and Judge of excessive drinking and inappropriate treatment of women in the early 1980s, among other accusations. Kavanaugh has called her accusations a “joke.” Judge has said he “categorically” denies the allegations.

Swetnick’s attorney, Michael Avenatti, said Saturday that his client had not been contacted by the FBI but was willing to cooperate with investigators.

Ford also has said Judge was in the room when a drunken Kavanaugh sexually assaulted her. Judge has said he will cooperate with any law enforcement agency that will “confidentially investigate” sexual misconduct allegations against him and Kavanaugh. Judge has also denied misconduct allegations.

Sanders spoke on “Fox News Sunday,” Conway appeared on CNN’s “State of the Union” and Graham and Hirono were interviewed on ABC’s “This Week.”