Judge Kavanaugh has issued a fresh rebuttal of the allegation.
In a series of tweets Friday, Trump cast doubt on Ford's charge, mentioning her by name for the first time: "I have no doubt that, if the attack on Dr. Ford was as bad as she says, charges would have been immediately filed with local Law Enforcement Authorities by either her or her loving parents". His Republican party accuses the Democrats of using Ford as a last-minute spoiler to try and wreck Kavanaugh's path to the highest court, where he would tilt the bench firmly to the right for possibly years to come.
Committee staff has been in negotiations with Ford's attorney, Democrat operative Debra Katz, for days about receiving testimony. "I go through this with them every single day in D.C".
Ford dismissed Whelan's theory in a statement late Thursday: "I knew them both, and socialized with" the other classmate, Ford said, adding that she had once visited him in the hospital.
Ford wished to remain anonymous, but made a decision to speak to the Post amid fears she was on the verge of being outed.
Senate Majority Leader Mitch McConnell, R-Ky., speaking to conservative activists at the Value Voters Summit in Washington on Friday morning, expressed confidence Kavanaugh would be confirmed.
Democratic Senator Chris Coons said Trump's comments about Ford were "unacceptable and beneath the presidency". Susan Collins has suggested she will vote for Kavanaugh unless Ford testifies.
However, Prof Ford has set out conditions for her appearance which have yet to be agreed by the Senate Judiciary Committee.
The split between Trump Jr. and Flake illustrates the differing approach that Republicans have taken in addressing Ford's accusations.
"Her strong preference continues to be for the Senate Judiciary Committee to allow for a full investigation prior to her testimony".
Kavanaugh has had a relatively smooth confirmation track until the allegations against him were reported last week. Ford says Judge was in the room, but Judge has denied the incident took place when they were all high school students. Kavanaugh and his wife also had received threats, a senior White House official said.
If Ford opts not to participate, Republicans could well dispense with the hearing to avoid giving Democrats a forum for peppering Kavanaugh with embarrassing questions.
"I will be there", he wrote Grassley in a letter.
To Hannity, Trump called it a "very sad situation", characterizing Kavanaugh as an "outstanding person". But Tuesday, she began insisting on an FBI investigation of her allegations and said other witnesses should also participate in a hearing.
President Donald Trump nominated Kavanaugh to the Supreme Court, and said he stands by his choice.
The confirmation fight comes just weeks before November 6 congressional elections in which Democrats are seeking to win control of Congress from the Republicans.
The FBI could interview Professor Blasey Ford, Mr Kavanaugh and others if Mr Trump asked it to reopen its background investigation, but the President has rejected that idea, saying the FBI has already done its work.
The Senate Judiciary Committee vote on Judge Kavanaugh had originally been scheduled for Thursday.
"We got a little hiccup here with the Kavanaugh nomination, we'll get through this and we'll get off to the races", he said in a call with fellow Republicans, the Nevada Independent reports.