Kavanaugh has repeatedly and categorically denied the allegations.
Ford alleges that Kavanaugh sexually assaulted her at a house party in the 1980s, when they were both teenagers at Washington-area private schools.
The letter says Ford "accepts" the committee's request that in the coming week she would "provide her first-hand knowledge of Brett Kavanaugh's sexual misconduct". Klobuchar and other Democrats had opposed Kavanaugh before Ford's accusation became public.
It was not immediately clear whether the Republican-controlled Judiciary committee would agree to more talks with Ford's team. "We are hopeful that we can reach agreement on details".
The Washington Post reports that one White House official said, "This is an ask to continue "negotiations" without committing to anything".
But some Republicans believe the agreement to appear, sent just minutes before a 2:30 p.m. deadline set by Chairman Charles Grassley, is a smokescreen to delay a vote on the nominee.
The official was not authorized to speak publicly about ongoing negotiations and spoke on condition of anonymity.
US President Donald Trump introduces his Supreme Court nominee judge Brett Kavanaugh (L) in the East Room at the White House in Washington, US, July 9, 2018.
Also Saturday, Vice President Mike Pence joined the chorus of renewed Republican support for Kavanaugh, telling a crowd of around 2,000 conservative activists at the Values Voter Summit that Kavanaugh "is a man of integrity, with impeccable credentials and a proven judicial philosophy" and that he would soon be confirmed.
Christine Blasey Ford has accepted the Senate Judiciary Committee's request to testify against Supreme Court nominee Brett Kavanaugh. Chuck Grassley of Iowa, is shrugging off responsibility for the extension onto the Senate's Democratic leader, Chuck Schumer.
Republicans say they have bent over backward to accommodate Ford's requests. A former Hennepin County Attorney, Klobuchar is also the only Minnesota lawmaker on the Senate Judiciary Committee, and she led the letter along with U.S. Sen.
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Ford's accusations of Kavanaugh's behavior 35 years ago and the unusually tense standoff over the terms of her appearance have captivated the nation as the appellate court judge's confirmation to the court hangs in balance. Before the 2016 presidential election, more than a dozen women accused Trump of making unwanted advances.
Grassley had said earlier that the panel would vote on Kavanaugh's confirmation on Monday unless a deal was reached with Ford's lawyers by a Friday night deadline.
Kavanaugh had seemed to gain momentum among Republican senators this week, with growing numbers saying it was approaching time to vote and those who'd voiced concern about Ford's charges stopping short of expressing opposition to Kavanaugh. Ford's attorney said, "our modest request is that she be given an additional day to make decision".
Last week Ford requested that the Federal Bureau of Investigation launch a probe into Kavanaugh's allegations, but was rejected by Grassley.
He also rejected her proposal that she testify after Kavanaugh, a position lawyers consider advantageous because it gives them a chance to rebut accusations.
Confirming Kavanaugh's nomination would cement conservative control of the Supreme Court and advance a White House effort to tilt the American judiciary farther to the right.
Grassley's stance underscored a desire by President Donald Trump and GOP leaders to usher the 53-year-old Kavanaugh onto the high court by the October 1 start of its new session and before the November elections, when Democrats are mounting a robust drive to grab congressional control.
Earlier, Trump ended a week of constraint and sarcastically assailed Ford, tweeting that if the episode was "as bad as she says", she or "her loving parents" surely would have reported it to law enforcement.
They were wrangling over several contentious details, including whether Ford would testify to the committee before or after Kavanaugh; whether the committee would subpoena a possible witness to the alleged assault, Kavanaugh's boyhood friend Mark Judge; and who would conduct the questioning.
Ford's supporters said McConnell's comments Friday morning proved that Republicans were not serious about hearing the California professor's side of the story and they were just inviting her to testify so as not to appear dismissive of her claims.
Grassley consented to other Ford demands, including that she be provided security and that Kavanaugh not be in the hearing room when she testifies.