In a letter to the committee, Ford's lawyers said that she "accepts" the request to provide "her first-hand knowledge of Brett Kavanaugh's sexual misconduct next week" after Republicans on the committee set a 2:30 p.m. deadline for her to say whether or not she would testify.
"We believe Dr. Blasey Ford and are grateful that she came forward to tell her story", the letter said.
The lawyers say they are "hopeful that we can reach agreement on details" of Ford's appearance.
Kavanaugh denies the allegations and has said he would testify to clear his name.
In a late-night tweet, Grassley said he "just granted another extension".
Grassley has been tweeting about the potential hearing regarding Dr. Christine Blasey Ford's allegations against Kavanaugh since September 19, saying that he and his colleagues wanted to hear from her and would "treat this situation with the sensitivity it deserves".
Ms Katz wrote that Ford "wishes to testify, provided that we can agree on terms that are fair and which ensure her safety".
He did not, however, say how long he would wait for Ford "to decide if she wants to proceed".
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Ford's lawyers and numerous opposition Democrats have repeatedly called for the Federal Bureau of Investigation to open a probe.
In backing away from his earlier deadline, Grassley underscored the sensitivity with which Senate Republicans have tried handling Ford.
Ford's decision to testify under oath will set off a fresh round of political fireworks as Republicans battle to get Kavanaugh confirmed in time to ascend to the Court before its October 1 opening session.
They have further energized Democrats, and women particularly, in a midterm election in which Republicans are struggling to court the female vote. Mr. Trump's searing reproach of the California psychology professor defied the Senate Republican strategy, and the advice of White House aides, of not disparaging her while firmly defending his nominee and the tight timetable for confirming him.
Although inferring otherwise, Whelan said he's not insinuating that the man he publicly named and shared photos of did anything wrong, or that Ford is now "mistakenly remembering" this man as Kavanaugh.
Grassley rebuffed other Ford requests, including calling additional witnesses.
Ms Ford says Mr Kavanaugh sexually assaulted her at a Maryland house party in the early 1980s when both were high school students.
A Washington Post profile of Ford, who is now married with two children, gave an account of how she struggled with the trauma of the alleged assault in 1982, undergoing therapy.