President Trump has said he wants the FBI to conduct a "very comprehensive investigation" into sexual assault allegations against his Supreme Court nominee - but not a "witch hunt".
US media reports earlier suggested the White House wanted to restrict the inquiry into Judge Brett Kavanaugh.
Mr Trump said he had requested that the FBI be given free rein, but added: "I'd like it to go quickly."
Judge Kavanaugh's friend Mark Judge has been interviewed by agents.
A lawyer for Mr Judge - a childhood friend of Mr Kavanaugh - said on Monday that his client's interview "has not been completed" yet.
Mr Judge's testimony is considered key to the investigation, as Professor Christine Blasey Ford says he was in the room when Brett Kavanaugh allegedly assaulted her at a house in 1982.
Mr Judge did not appear before the Senate Judiciary Committee in person, but said in a statement: "I do not recall the party described in Dr Ford's letter."
When will the Senate vote on Kavanaugh?
On Monday, Senate Majority Leader Mitch McConnell said the Senate would vote this week on whether to confirm Judge Kavanaugh to the Supreme Court.
"The goal posts keep shifting," he said on the Senate floor as he accused Democrats of devising endless delays. "But the goal hasn't moved an inch."
"The time for endless delay and obstruction has come to a close."
Mr McConnell did not specify when exactly the vote would be held, but it is widely expected to be on Friday - the deadline for the FBI to finish its inquiry - or the following day.
Who is the FBI speaking to?
The FBI is expected to interview Judge Kavanaugh and some of the women who have accused him of sexual misconduct - including Prof Ford, who testified last week to the Senate Judiciary Committee.
Quoting an unnamed senior US official, NBC reported that the FBI's witness list does not include Julie Swetnick, the third accuser to come forward with a claim against Mr Kavanaugh.
US reports also say former classmates of the judge's who have stressed his heavy college drinking are not on the witness list.
However, the New York Times earlier reported that a contemporary who accused the judge of lying under oath about his relationship with alcohol plans to speak to the FBI on Monday.
Because the agency isn't running a criminal investigation, but performing a background check at the request of the White House, it is the White House that defines the inquiry's parameters.
The president told reporters on Monday: "The FBI should interview anybody that they want within reason, but you have to say within reason."
He went on: "They should also be guided, and I'm being guided, by what the senators are looking for."
What are the drinking allegations?
Professor Charles Ludington, who teaches at North Carolina State University, said he had seen Judge Kavanaugh slurring his words and staggering after excessive alcohol consumption while at Yale.
Outside his home on Monday, Prof Ludington told reporters "unequivocally" that Judge Kavanaugh "has not told the truth" in denying the possibility that he blacked out from drinking.
But he added: "I never saw him passed out but I saw him quite drunk."
The White House rebutted these claims with statements from two former Yale classmates of Judge Kavanaugh.
Chris Dudley and Dan Murphy said they had never seen the nominee black out at college or behave inappropriately with women.
How have Democrats reacted?
On Monday nine of the 10 Democrat Senators on the Senate Judiciary Committee wrote to FBI Director Christopher Wray with a list of 24 people they believe should be interviewed. They called on the FBI to interview all three of the judge's accusers.
Democrats have requested copies of all the FBI's witness interviews, and the names of any who decline to co-operate.
Judge Kavanaugh denies the claims of his accusers:
- Psychology lecturer Prof Ford, the first woman to come forward, says Judge Kavanaugh tried to remove her clothing, pinned her to a bed and covered her mouth at a house party in 1982, when she was 15 and he was 17
- Deborah Ramirez, a student at Yale at the same time as Judge Kavanaugh, says he exposed himself to her during a college drinking game
- Julie Swetnick says she went to house parties attended by Judge Kavanaugh in the early 1980s, where she said he and his friends had tried to "spike" girls' drinks
What's likely to happen at the vote?
It's not currently clear whether the Republican leadership has secured enough votes to ensure Judge Kavanaugh's confirmation.
The party's narrow 51-49 majority means that if all Democratic senators vote against the nominee, Republicans can only afford one defection.
In that instance, Vice-President Mike Pence has the casting vote, and would vote in Mr Kavanaugh's favour.
The FBI investigation was launched at the urging of Republican Senators Jeff Flake, Susan Collins and Lisa Murkowski.
How teens are talking about sex in the #MeToo age
