GOP Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style MORE (Ariz.) on Monday said that he wants the FBI's investigation into sexual assault allegations against Supreme Court nominee Brett Kavanaugh to be "fulsome," adding that it's "no good" if it is just to give senators "cover."

"We certainly want the FBI to do a real investigation and we are working to make sure that that happens," Flake said at the Forbes "30 under 30" summit, noting that he's talking with colleagues and the White House counsel's office.

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He added that the FBI's investigation should be "up to standard" and that any "current, credible" allegation should be investigated.

"It does no good to have an investigation that just gives us more cover, for example. We actually need to find out what we can find out," Flake said when asked if he would continue his threat to vote “no” on Kavanaugh if the investigation doesn't meet his standard.

Sen. Jeff Flake says "we certainly want the FBI to do a real investigation" on Brett Kavanaugh: "It does no good to have an investigation that just gives us more cover...we actually need to find out what we can find out." https://t.co/pWOU760blC pic.twitter.com/duhBTNFplP — ABC News (@ABC) October 1, 2018

Flake led a group of moderate senators late last week in demanding that the FBI be given a week to investigate the allegations against Kavanaugh, effectively delaying the Senate's vote on the nomination.

Shortly after Flake's remarks, The New York Times reported that the White House has told the bureau that it could interview anyone it deems appropriate as long as the investigation is finished by the end of the week.

The White House has faced some backlash by Democrats after NBC News reported that it had provided a scope for the investigation to the FBI that did not include Julie Swetnick, the third woman to accuse Kavanaugh of sexual misconduct.

Swetnick alleges that Kavanaugh was present at a party where a "gang rape," which she was a victim of, took place.

She came forward after Christine Blasey Ford and Deborah Ramirez both went public with their allegations against Kavanaugh. Ford told The Washington Post that at a party in the early 1980s Kavanaugh pinned her to a bed, groped her and tried to remove her clothing.

Ramirez told The New Yorker that Kavanaugh exposed himself to her while the two were students at Yale University.

Kavanaugh has fiercely denied all of the allegations.