California college professor Christine Blasey Ford wants the FBI to investigate her claim Kavanaugh assaulted her when they were teenagers, something Kavanaugh denies.
After initially suggesting a private conference call on the matter would suffice, Senate Judiciary Committee Chairman Chuck Grassley said his panel would hold a hearing next Monday "to provide ample transparency".
Meanwhile Mr Trump has said he is not anxious about what his former campaign chairman Paul Manafort, who is co-operating with the United States special counsel's probe into Russian election meddling, will tell prosecutors, as long as he is truthful.
He has also cast fresh doubt on whether the alleged attack even happened. "I just want to say to the men in this country: Just shut up and step up".
"This incident did happen", the letter said.
Ford's lawyers say she has been subject to death threats as a result of her allegations against Kavanaugh. That this courageous woman is receiving death threats and has been forced to flee with her family is appalling and heartbreaking.
Whether Kavanaugh and Ford testify under oath, and to what details, has enormous stakes for President Donald Trump and the November 6 midterm elections - not to mention American men, women, teenagers, parents, schools and anyone who rises to the top of a profession in the #MeToo era. The president said he was "totally supporting" Kavanaugh and rejected calls for the FBI to investigate the accusation.
The New Yorker magazine says Ford sent a letter about the allegation to Democrats. Moderate Republican Lisa Murkowski of Alaska told reporters: "If she isn't going to be part of the hearing, that would be a very interesting and unfortunate turn of events".
"You have stated repeatedly that Dr Ford wants to tell her story". That underscores a desire to avoid antagonizing female voters at a time when the #MeToo movement has made sexual abuse a major political dynamic.
Trump signs order to impose sanctions for U.S. election meddling
The public will be informed of interference activity when sanctions occur, Bolton said Wednesday on the conference call. The order, which will allow new sanctions against Russian or other foreign actors, was inked on Wednesday morning.
That clashes slightly with President Donald Trump and Senate Judiciary Committee Chairman Chuck Grassley's (R-IA) talking points about the FBI: They've said it's not the bureau's "thing" to look into investigations like Blasey Ford's, and that Kavanaugh's background probe is "closed".
The former Democratic presidential nominee said on MSNBC on Tuesday the relevant precedent is the FBI's investigation of Anita Hill's sexual-harassment allegation against Clarence Thomas in 1991. "It demands a thorough and independent investigation before the Senate can reasonably vote on Brett Kavanaugh's nomination to a lifetime seat on the nation's highest court".
McConnell, who is determined to deliver his second conservative Supreme Court justice in two years, now must navigate a treacherous pass.
Earlier on Monday, Republican leaders displayed no willingness to delay a Judiciary panel vote that Grassley had planned for this Thursday to advance the nomination. Kavanaugh has denied Ford's allegation and has said he's willing to appear before the committee.
No. 2 Senate Republican leader John Cornyn of Texas was one of the few Republicans who openly questioned Ford's version of events. Thomas denied Hill's account and was confirmed to the Supreme Court.
But the senator said Tuesday that he has been unable to get in contact with Ford and that she has yet to agree to testify before the committee.
If Ford opts not to testify, Kavanaugh's chances for confirmation in the Republican-led Senate could be boosted, with senators in Trump's party so far remaining largely supportive.