Kavanuagh has repeatedly denied the allegations.
Christine Blasey Ford, who alleged Supreme Court nominee Brett Kavanaugh sexually assaulted her when they were teenagers, told the Senate Judiciary Committee she is open to testify next week if they can "ensure her safety" and offer "terms that are fair". At first, she said she would not testify until the FBI had investigated, but then said Thursday through her attorney that she would agree to appear, but not when the Senate Judiciary Committee meets Monday.
Chuck Grassley, the committee's Republican chairman, on Wednesday sent a letter to Ford's lawyers giving her until 10am (14:00 GMT) on Friday to submit prepared testimony if she meant to show up on Monday. Kavanaugh, who has strongly denied the claims, has already agreed to appear.
"It is not the FBI's role to investigate a matter such as this", wrote Grassley, who also sent a letter to committee Democrats formally rejecting their bid for the FBI to investigate.
After going through psychotherapy, Ford said, she now understands the incident as a trauma that has had lasting impact on her life.
In their letter, Ford's attorneys had further stated that Ford wished the FBI to investigate her claims before he came before the committee.
United States ready to negotiate with North Korea 'immediately': Pompeo
His parents had fled from the North during the war, sailing for three days on the deck of a US ship packed with refugees. Special Representative for North Korea Stephen Biegun in Vienna, Austria, "at the earliest opportunity".
Ford had said in a letter through her lawyers on Tuesday evening that she wanted an FBI investigation into the matter before she appeared before the Senate committee tasked with reviewing Kavanuagh's nomination.
Ford's lawyers say she has been subject to death threats as a result of her allegations against Kavanaugh. They said Ford's "strong preference" is that "a full investigation" be completed before her testimony, but stopped short of demanding an FBI probe and seemed to suggest that she would testify without one.
The Constitution assigns the Senate, and only the Senate, with the task of advising the President on his nominee and consenting to the nomination if the circumstances merit. After scathing books from both his inner circle (Omarosa Manigault Newman's Unhinged) and some less close to him (Bob Woodward's Fury) were released, his Supreme Court nominee came under fire.
With Republicans fearful that Democrats could wrest control of the U.S. House of Representatives and even the Senate from them in November elections, Trump urged his supporters to get out and vote for the party's candidates, saying the economic measures he has put in place could be hanging in the balance.
Both have called on Judge Kavanaugh and Prof Ford to testify under oath. Feinstein contacted the Federal Bureau of Investigation, which sent the letter to the White House for inclusion in Kavanaugh's background file, after redacting Dr Ford's name.
Ford wants Kavanaugh to testify first and then she will tell her story to the committee, a committee staffer said. Nevada Sen. Dean Heller, for example, said in March that he believed it would turn out voters and help them turn back a potential midterm loss. "This strikes us as simply a check-the-box exercise in a rush to confirm Judge Kavanaugh". Some critics have posted allegations against Ford on the internet that have been debunked.
"She shouldn't be bullied into it", said Senator Kirsten Gillibrand, a New York Democrat, at a news conference with alumna from Holton-Arms, the private girls' school Ford attended at the time of the alleged attack more than three decades ago.