The statement is signed by attorney's Debra Katz and Lisa Banks.
Ford's agreement comes one day after Grassley again extended the deadline he gave Ford to decide whether or not she would testify to his committee and explain her allegations in detail. "It's a clever way to push off the vote Monday without committing to appear Wednesday".
The aide said Ms Katz told the committee by telephone that Ford didn't want Mr Kavanaugh in the room when she testified.
"Its sole goal is to bully Dr Ford and deprive her of the ability to make a considered decision that has life-altering implications for her and her family", the professor's lawyer Debra Katz said on Friday evening, asking for another day to decide.
Senate Judiciary Chairman Charles E. Grassley (R-Iowa) is in charge of setting up such a hearing.
The email from Ford's lawyers says she agrees to "provide her first-hand knowledge of Brett Kavanaugh's sexual misconduct next week".
Kavanaugh denies the allegations and has said he would testify to clear his name.
"I ask that she bring those filings forward so that we can learn date, time, and place!"
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They rejected conditions sought by accuser Christine Blasey Ford, including her request to call other witnesses in addition to her and Mr Kavanaugh. I hope you understand. "It's not my normal approach to b indecisive", Grassley said.
The GOP letter to Ford's lawyers said Kavanaugh and his family have received death threats too, "And they're getting worse each day".
Grassley turned down Ford's request that only senators, not attorneys, be allowed to ask questions.
Ford's lawyers repeated their call for the matter to be dealt with in a rigorous investigation, not what Democrats describe as a rushed hearing in the Republican-dominated Senate aimed at confirming Kavanaugh as quickly as possible. We are unwilling to accommodate your unreasonable demands.
Grassley also complained about not having heard from Ford regarding her potential Senate testimony.
She alleged a "stumbling drunk" 17-year-old Kavanaugh sexually assaulted her at a Maryland house party in 1982 when both were in high school.
Grassley did not immediately respond to the letter, but a senior White House official told Fox News that it represented a request to continue negotiations about the terms on which she testifies without any firm commitment.
Allegations from a university professor, Christine Blasey Ford, emerged in the U.S. media last week.