The woman whose sexual assault allegation threatens to bring down President Donald Trump's Supreme Court nominee has agreed to testify in the Senate, her lawyers said Saturday, setting up a dramatic showdown next week.

Christine Blasey Ford's decision followed days of negotiations and came after Trump turned against her and said her accusation could not be true.

After the Senate Judiciary Committee received a message from Ford's lawyers, several members confirmed she had accepted their committee's request to testify.

"Dr. Blasey Ford will testify next week. She has shown tremendous courage in the face of death threats and harassment and deserves respect as final details for the hearing are worked out," Democratic Senator Dianne Feinstein tweeted.

Hours later, multiple outlets including Politico and The Daily Beast reported the hearing would take place on Thursday, citing sources familiar with a phone call between the committee and Ford's lawyers.

The committee's Republican leader Chuck Grassley had wanted the hearing to take place on Wednesday, but Ford asked that it be held on Thursday at the earliest and to be able to call as a witness a man she says was present during the assault.

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.

Earlier, the panel had given the California professor until 2:30 pm (1830 GMT) to decide whether to appear, after she rejected a Friday evening deadline imposed by Grassley.