"I feel so badly for him that he's going through this, to be honest with you", Reuters quoted Trump as saying.
Trump repeated earlier statements that he is in favour of allowing both the accuser, Christine Blasey Ford, and Kavanaugh to speak before the Senate Judiciary Committee. Grassley blamed Democrats for not previously disclosing the claim by Ford, who had sought to remain anonymous before ultimately agreeing to be publicly identified.
Republicans had also displayed no willingness to delay a Judiciary panel vote that Grassley had planned for this Thursday to advance the nomination.
Thomas, the court's second black justice, was ultimately confirmed, but only after a nasty televised hearing in which Hill faced pointed questions from Republican senators and the nominee said he was the victim of "a high-tech lynching for uppity blacks".
"I am willing to talk to the Senate Judiciary Committee in any way the Committee deems appropriate to refute this false allegation, from 36 years ago, and defend my integrity", he said in the statement.
Kavanaugh responded through the White House with a categorical denial.
She said Kavanaugh, "stumbling drunk", threw her down on a bed, grinding his body against hers and trying to pull off her one-piece bathing suit and the clothing she was wearing over it. Ford said when she tried to scream, he put his hand over her mouth. Blasey Ford asked for confidentiality, and the allegation was not made public - until this past weekend.
"If she shows up and makes a credible showing, that will be very interesting and we'll have to make a decision", Trump told reporters as he left the White House for a trip to the Carolinas.
"That would be quite something if she decided she did not want to testify", Corker said. Ask the questions - even the uncomfortable ones - that help them and us get the best sense possible of what really happened and what (if anything) it tells us about Kavanaugh.
He led the state Senate last fall when accusations of widespread misconduct rocked the Capitol.
Shortly before Grassley's announcement, the senator said there would be private, telephone interviews of Kavanaugh and Ford conducted by committee staffers. Even if the allegations are true, she does not believe they should disqualify the nominee, "because I don't think that's the kind of life that he's led".
Don Stewart, a spokesman for Senate Majority Leader Mitch McConnell of Kentucky, said the Republican senator doesn't have any immediate comment about the matter.
Mr Kavanaugh has "categorically and unequivocally" denied the allegations. "I did not do this back in high school or at any time".
And he will do that in a scheduled hearing Monday, in what Democrats worry will be a replay of another he-said, she-said exercise in 1991 when Anita Hill came forward with sexual harassment allegations against then-Supreme Court nominee Clarence Thomas. He accused Democrats of being "lousy politicians, but good obstructionists" in their efforts to derail Kavanaugh's confirmation to a lifetime appointment on the country's highest court.
Kavanaugh's potential impact on the abortion debate is a risk to the GOP's already lackluster standing with women, and the sexual assault allegation could make things worse. "I hope Republican Voters, and others, are watching and studying, the Democrats Playbook".
"Not only do women like Dr. Ford, who bravely comes forward, need to be heard, but they need to be believed. If she doesn't show up, that would be unfortunate", he said. "I am, anyway, and I think most of us are".
"In fact, I have no memory of this alleged incident", Judge said in his statement to the committee.