Judge Brett Kavanaugh pauses while delivering his opening statement during his Supreme Court confirmation hearing before the Senate Judiciary Committee in the Hart Senate Office Building on Capitol Hill, September 4, 2018 in Washington, DC.

Christine Blasey Ford, the woman who has accused President Donald Trump's Supreme Court nominee Brett Kavanaugh of sexual assault, said an FBI investigation should be "the first step" before she testifies before the Senate Judiciary Committee.

However, Sen. Chuck Grassley, the Iowa Republican who chairs the panel, said Tuesday night there is no reason to delay the process any further. Grassley canceled Thursday's planned committee vote on Kavanaugh and scheduled a hearing on the allegations for Monday.

The latest developments escalated an already intense drama in the nation's capital, as Republicans, who had been on track to quickly confirm Kavanaugh with their thin 51-49 Senate majority and likely establish a conservative majority on the top court for decades to come. Ford's accusations against the federal appellate judge, however, have thrown the process into turmoil.

Republican senators still want to move the process along, but they have been hesitant to show any antipathy toward Kavanaugh's accuser. Trump has also been remarkably cautious in his comments about the situation. The president, who is known for scorched-earth tactics when he or someone in his circle stands accused of something, has continued to praise and back Kavanaugh, but he has also expressed a desire to hear out Ford, as well.

Yet Wednesday morning, Trump cast doubt on Ford's accusations, telling reporters that it is "very hard for me to imagine that anything happened."

Ford, a 51-year-old research psychologist who lives in California, came forward on Sunday and publicly accused Kavanaugh of sexual assault during an alleged drunken encounter when they were both teenagers more than three decades ago.

Kavanaugh has denied those allegations and said he was willing to testify before the Senate to "refute" accusations of sexual misconduct against him.

"An FBI investigation of the incident should be the first step in addressing her allegations," Ford's lawyers wrote in a letter to Grassley on Tuesday.

Ford "wants to cooperate," the attorneys said. However, the hearing is scheduled for Monday, "six short days from today and would include interrogation by Senators who appear to have made up their minds that she is 'mistaken' and 'mixed up.'"

Her "worst fears have materialized," Ford's lawyers said. "She has been the target of vicious harassment and even death threats."

"While Dr. Ford's life was being turned upside down, you and your staff scheduled a public hearing for her to testify at the same table as Judge Kavanaugh in front of two dozen U.S. Senators on national television to relive this traumatic and harrowing incident," Ford's lawyers said.

Grassley, in turn, expressed sympathy for Ford, but still persisted in seeking her testimony.

"Nobody should be subject to threats and intimidation, and Dr. Ford is no exception," Grassley said in a statement. "These are serious allegations and Dr. Ford deserves to be heard."

Republicans have focused their ire on Democrats as the accusations only came to light after Kavanaugh's confirmation hearings before the Judiciary Committee.

Sen. Dianne Feinstein received a letter from Ford in late July which alleged that Kavanaugh had drunkenly held Ford down on a bed and attempted to remove her clothes when they were in high school in the 1980s. Ford claimed that Kavanaugh's friend, Mark Judge, who was also in the room at that time, jumped on them.

Judge has also denied Ford's allegations.

"A full investigation by law enforcement officials will ensure that the crucial facts and witnesses in this matter are assessed in a non-partisan manner," Ford's lawyers wrote.

— CNBC's Kevin Breuninger contributed to this report.