Supreme Court nominee Judge Brett Kavanaugh testifies before the Senate Judiciary Committee on the third day of his Supreme Court confirmation hearing on Capitol Hill September 6, 2018 in Washington, DC.

President Donald Trump's Supreme Court nominee Brett Kavanaugh said Monday that he is willing to testify before the Senate Judiciary Committee once again in order to "refute" an allegation of sexual misconduct against him.

"This is a completely false allegation. I have never done anything like what the accuser describes—to her or anyone," Kavanaugh, 53, said in a statement.

A White House official later on Monday told NBC News denies he even attended the party in question.

On Sunday, California professor Christine Blasey Ford, 51, came forward publicly to accuse Kavanaugh of sexual assault during a drunken encounter when they were both teenagers.

Kavanaugh's potential return to Capitol Hill for another grilling from lawmakers sets up a high-stakes game of he said-she said, as Ford has also signaled a willingness to state her allegations in congressional testimony.

After Ford spoke with The Washington Post in a report published Sunday, lawyer Debra Katz told news outlets that Ford is open to speaking before the Senate Judiciary Committee, which is scheduled to vote on Kavanaugh's nomination this week.

Ford "will do whatever is necessary to make sure that the Senate Judiciary Committee has the full story and the full set of allegations to allow them to make a fully informed decision," Katz said.

Ford had originally requested anonymity in a letter she sent to California Rep. Anna Eshoo detailing the allegation. Eshoo passed Ford's letter to Senate Judiciary Committee ranking member Dianne Feinstein, D-Calif. Feinstein referred the letter to federal investigators.

Mark Judge, a classmate of Kavanaugh's who Ford says was a participant in the alleged assault, told The New Yorker that he has "no recollection" of the incident.

In a statement Monday, Senate Judiciary Chairman Chuck Grassley, R-Iowa, criticized Feinstein and other Democrats on the committee for withholding the allegations until "the eve of the committee vote, after the vetting process had been completed."

Grassley said his "standard procedure" would be to conduct follow-up calls with Kavanaugh and Ford, but Feinstein's office "refused" to help him schedule those calls.

Feinstein responded: "There's a lot of information we don't know and the FBI should have the time it needs to investigate this new material. Staff calls aren't the appropriate way to handle this."

As the initially cryptic reports about Ford's letter grew in detail, some Republican lawmakers began to call for more time to investigate the allegations.

"If they push forward without any attempt with hearing what she's had to say, I'm not comfortable voting yes," said Sen. Jeff Flake, R-Ariz., an occasionally vocal critic of Trump's who is retiring at the end of his term. Flake is a member of the the Judiciary Committee, which has not yet rescheduled a vote on Thursday to advance Kavanaugh's nomination.

Tennessee Sen. Bob Corker, another Republican Trump critic who is also retiring, said that delaying the committee vote "would be best for all involved, including the nominee."

--CNBC's Brian Schwartz contributed to this report.