"Dr. Ford accepts the Committee's request to provide her first-hand knowledge of Brett Kavanaugh's sexual misconduct next week", says the letter, which is signed by Ford's lawyers Lisa Banks and Debra Katz.
Trump, speaking in NY where he was attending the United Nations annual assembly, threw his full weight behind Kavanaugh whose once straightforward progress to the nation's highest court has been hit by two bombshell accusations of sexual misconduct from his school and university days.
The latest accusation comes from Deborah Ramirez, who in a story published in The New Yorker alleges Kavanaugh exposed himself to her during a drunken party at Yale when both attended college there in the 1980s.
The Republican-led committee had insisted that if Ford missed a Friday night deadline to respond to the panel's latest offer, lawmakers would hold a vote Monday on recommending Kavanaugh's nomination for the full Senate to consider. She referred to Ford as a "survivor of attempted rape" - even though Kavanaugh has denied her accusation, and every witness Ford has mentioned has contradicted her account.
"I will not be intimidated into withdrawing from this process", Kavanaugh, a conservative federal appeals court judge nominated by Trump in July for a lifetime job on the top USA court, wrote in a letter to the Republican-led Senate Judiciary Committee, which is overseeing the confirmation process.
The combative tone by Kavanaugh and Trump came a day after a second allegation emerged.
"Senate Democrats and their allies are trying to destroy a man's personal and professional life on the basis of decades-old allegations that are unsubstantiated and uncorroborated", Mr McConnell added. The ranking Democrat on the committee, California Senator Dianne Feinstein has requested the cancellation of a Thursday hearing at which another woman was to testify about an alleged assault by the nominee.
A White House spokeswoman says the administration stands by the nominee, labelling the allegation "the latest in a co-ordinated smear campaign by the Democrats created to tear a good man down".More news: Earl Thomas trade rumors: Seahawks S asked about chatter
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He began his career as a clerk to Anthony Kennedy, the justice long considered a critical swing vote on the Supreme Court, and will succeed him on the bench if confirmed.
Trump, speaking to reporters on his way into the United Nations on Monday morning, said Kavanaugh "is an outstanding person, and I am with him all the way".
"I will not be intimidated into withdrawing from this process".
Journalists listen to opening statements during Brett M. Kavanaugh's Supreme Court confirmation hearing on Capitol Hill on September 4, 2018.
Republicans have slammed the timing of the accusations as a political smear campaign aimed at derailing Kavanaugh's confirmation.
Grassley spokesman Taylor Foy accused Democrats of with holding information about allegations for political reasons but said the committee will "attempt to evaluate these new claims".
When The New Yorker first contacted Ms Ramirez, it said she was reluctant to come forward, partly because of gaps in her memory because she had been drinking at the time of the incident.
The White House is approaching Ford's potential testimony with trepidation, nervous that an emotional performance might not just damage Kavanaugh's chances but could further energize female voters to turn out against Republicans in November.
They also agreed to increased security for Ford and Kavanaugh. The committee said all three told investigators that they had no recollection of the evening in question.