But sources close to Ford say that she may still not agree to the Senate committee's primary request: that she testify about Kavanaugh's alleged sexual misconduct under oath.
"Despite actual threats to her safety and her life, Dr. Ford believes it is important for senators to hear directly from her about the sexual assault committed against her", the lawyers' statement reads.
Kavanaugh, who strongly denies the assault allegation, has said he wishes to testify as soon as possible to clear his name.
The tentative deal capped a day of frenetic developments, with time running out for Trump to get his hand-picked conservative judge confirmed - thereby tilting the Supreme Court firmly to the right for years to come - before November elections when Republicans risk losing control of Congress.
The committee earlier Friday had set a deadline of 5 p.m. ET for Ford to decide, later extending that to 10 p.m.
"Despite actual threats to her safety and her life, Dr Ford believes it is important for senators to hear directly from her", said a statement from Christine Blasey Ford's lawyers, quoted by U.S. media. It says she will "provide her firsthand knowledge" but it doesn't say how.
He acknowledged that lawmakers will "probably not" be able to know the truth of Ford's decades-old accusation that Kavanaugh assaulted her at a house party when they were teenagers.
Republicans, who hold a paper-thin majority in the Senate, can ill afford defections if Kavanaugh is to be approved.
Pakistan's Khan to visit Riyadh on first trip
Why are we so cruel to these people? He went on: "They are humans ". The question is that he was propped up by the Army .
"I will listen, but I'm not going to play a game here and tell you this will wipe out his entire life", Graham said.
Grassley and other Republican leaders were gearing up to muscle Kavanaugh's confirmation through without testimony from the accuser, until her lawyers on Thursday began negotiations for the hearing.
The Judiciary panel's top Democrat expressed fury at Grassley's negotiating position with Ford and maintained Democrats' effort to build the battle into a larger election-year question about the treatment of women.
On Friday, Mr Grassley had rejected concessions Ms Ford wanted if she is tell her story publicly before the committee.
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.
'There have been a lot of things said about the alcohol that was consumed by the judge as well as by others in his school. She has said that Ford feels rushed and is busy meeting with Federal Bureau of Investigation agents over death threats. Multiple senior members of the committee are pushing for one, while others are less interested, according to the source, making it unclear whether this will make it into the final proposal to Ford. "I'm shocked and appalled by the Republicans' refusal to wait 24 hours for a hearing and instead rush forward with a vote on Monday".
Fox News anchor Chris Wallace asked if Graham has "an open mind on this" and if Ford could say anything that would change his mind in her hearing.
"All four of these individuals have provided statements to the Senate Judiciary Committee denying any knowledge of the incident or even having attended such a party", White House spokeswoman Kerri Kupec said in a statement late on Saturday.
Ford, a research psychologist at Palo Alto University, is still hoping the Senate Judiciary Committee will meet several conditions.