However, top Republicans seemed to be trying to limit any new testimony by Kavanaugh and his accuser, Christine Blasey Ford, to telephone interviews.
Kavanaugh adamantly denies the allegation, as does the other man named by Ford, Mark Judge.
"The Chairman and Ranking Member routinely hold bipartisan staff calls with nominees when updates are made to nominees' background files", Foy said in a statement.
In a statement on Monday, Kavanaugh called the allegation by Ford, who is a college professor, "completely false".
Christine Blasey Ford, a 51-year-old California professor, accused Kavanaugh of groping her and trying to take her clothes off when they were both attending suburban Maryland high schools in the early 1980s.
Prof Ford spoke of the alleged attack a couple of times over the subsequent decades, including during therapy.
"I talked to [Kavanaugh] on the phone today...[he said] he didn't do that, and he wasn't at the party", Hatch said.
Debra S. Katz, the attorney for the accuser, said Ford was willing to tell her story publicly to the Judiciary panel but no lawmakers had yet contacted her. Katz denied that Ford, a Democrat, was politically motivated.
What does Ford say happened? .
Now, several Senate Democrats and Republicans say Kavanaugh's confirmation proceedings, which are set to take place this week, should be halted until they can question Ford and Kavanaugh.
Democrats are now demanding a delay on the Kavanaugh vote in light of Ford's story.
Because Trump's fellow Republicans control a slim 51-49 majority in the Senate, Democrats can not stop Kavanaugh's appointment unless some Republicans make a rare decision to break with their party and vote against Trump. She did not announce what the accusations against him are or who is making them.
A spokesperson for the Koch-backed Americans for Prosperity, which has already spent heavily on pro-Kavanaugh ads, said in a statement Monday that "any allegation of this type should be taken seriously, however, we are not going to speculate on media reports". According to USA media, some Republicans on the panel also said the vote should be delayed until the committee can hear Ford's testimony. One of the "oddest episodes", she said, involved an exchange in Thomas' office when he reached for a can of Coke and asked, "Who has put pubic hair on my Coke?"
"I thought he might inadvertently kill me", Ford said.
This episode recalls another high-stakes confirmation battle more than 25 years ago, when then-judge Clarence Thomas faced sexual harassment allegations during his Supreme Court hearings.
Collins, a key uncommitted senator on Kavanaugh's nomination, said she doesn't know enough yet to say whether she believes Ford's allegations but that having the opportunity to question her would help her make an assessment.
The Senate Judiciary Committee has completed its hearings on Kavanaugh and plans to vote on Thursday on his nomination.
Kavanaugh's nomination had already sharply divided the Senate along party lines. Susan Collins (R-Maine) told reporters Monday on Capitol Hill, calling for testimony from Kavanaugh and Ford. Now, with 23 women in the Senate - including four on the judiciary committee - and the backdrop of the #MeToo movement, Kavanaugh's future as a Supreme Court justice is in uncharted territory.
"We are women who have known Brett Kavanaugh for more than 35 years and knew him while he attended high school between 1979 and 1983", the women wrote in a letter to Senate Judiciary Committee members Chuck Grassley (R-Iowa) and Dianne Feinstein (D-Calif.).