They said they want the findings released publicly, and want an in-person briefing for senators with the agent who is leading the new background check.
Schumer had made the 24-hour demand in a letter to the top Republican, Sen.
Earlier on Tuesday, Iowa senator Joni Ernst, one of six Republican women in the chamber, said she plans to vote for Kavanaugh unless the investigation corroborates the allegations against him. The FBI does, however, prepare detailed investigation notes from witness interviews.
Judge has denied the allegations, as has Kavanaugh.
President Donald Trump told reporters at the White House on Monday that the FBI had the authority to interview anyone it desired, pushing back against charges by Senate Democrats that the White House was limiting the scope of the investigation.
"What message that sends to women in America is that we are innocent until proven guilty in this country", said Ernst.
U.S. reports also say former classmates of the judge's who have stressed his heavy college drinking are not on the witness list.
Appearing at a forum sponsored by The Atlantic, Flake said he was concerned about some of Kavanaugh's sharp interactions with Democratic senators on the Judiciary Committee last week.
McConnell's combative remarks about Democrats came as Trump and lawmakers await the FBI's reopened background check on the accusations against the 53-year-old jurist.
Central to the Supreme Court confirmation saga of the Trump administration has been the fact that no individual prospect from his pre-vetted list of 25 prospects is indispensable.
The FBI is investigating claims made by Christine Blasey Ford that the Supreme Court nominee sexually assaulted her in the 1980s. She had said Monday night that the interview was not completed.
The White House instructed the Federal Bureau of Investigation to interview anyone it deems relevant to the inquiry, but required the work to be done by Friday, according to a source.
Mr Kavanaugh's confirmation hinges on a handful of key Republican and Democratic senators who have not yet fully tipped their votes. Those documents, once completed, should be made promptly available to all senators well before a final vote on Kavanaugh takes place.
In a statement to the ME newspaper the Portland Press Herald, a spokeswoman for Collins said she, Murkowski and Flake "advocated for the additional background investigation because she believed that it could help the senators evaluate the claims that have been brought to the Judiciary committee".
The votes of the three Republicans and those of red-state Democrats Joe Manchin of West Virginia and Heidi Heitkamp of North Dakota will largely determine whether Mr Kavanaugh is confirmed.
Heitkamp, meanwhile, noted that Trump himself called for a "broader" FBI investigation into the allegations.
Collins, who was riding with Murkowski on an underground Senate train, smiled and told her colleague, "Good answer".
"He has grossly mischaracterized his relationship with alcohol", Schumer said, characterizing Kavanaugh as someone who "tiptoes around the truth".
"I have absolutely no doubt after reviewing Dr. Ford's testimony that she has suffered from something very traumatic in her lifetime, but simply the corroboration wasn't there with even the witnesses that she brought forward", Ernst said.
Sen. Mazie Hirono, a Democrat from Hawaii, said, "We're going to put a conspiracy theory believer on the court?" All of them", Mr. Schumer told reporters, adding, "We have nothing to do with delay.
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