DEMOCRATS in the US Senate are investigating a new bombshell allegation of sexual misconduct against President Donald Trump’s nominee for the Supreme Court, The New Yorker reports.

Deborah Ramirez, 53, told the magazine Brett Kavanaugh exposed himself to her during a college party at Yale University in the 1980s, thrust his genitalia in her face and caused her to touch them without her consent.

A new allegation against Supreme Court nominee Brett Kavanaugh surfaces, this time from his years at Yale. The latest from me and @JaneMayerNYer: https://t.co/o8nTmjw2Vg — Ronan Farrow (@RonanFarrow) September 23, 2018

Kavanaugh denied the incident occurred, calling it “a smear, plain and simple.”

“The people who knew me then know that this did not happen, and have said so,” he said in a statement published by the magazine.

It comes as lawyers for Kavanaugh’s first accuser, Christine Blasey Ford, and the Senate Judiciary Committee reached agreement for a public hearing on Thursday, as talks continued to resolve potentially make-or-break details, such as potential witnesses who could corroborate her decades-old sexual assault claim.

Ms Ford committed to an “open” hearing after negotiators convened a call on Sunday, her lawyers said in a statement.

A spokesman for the committee’s chairman, Republican Senator Chuck Grassley confirmed the meeting would be set at 10am (12am AEST) on Thursday.

“We’ve made important progress,” said Ms Ford’s lawyers Debra S. Katz, Lisa J. Banks, and Michael R. Bromwich.

“Dr Ford believes it is important for senators to hear directly from her about the sexual assault committed against her. She has agreed to move forward.”

Terms of their appearances are still being negotiated, but several details have been resolved.

Ms Ford agreed that she will testify after Mr Kavanaugh, rather than going first, as she had preferred, according to a source familiar with the talks, but was unauthorised to discuss the talks publicly and was granted anonymity.

But who will be asking the questions remains unresolved, the lawyers said. Republicans have been trying to hire an outside female counsel who could take over the questioning. The 11 senators on the Republican side of the dais are all men, which could send an unwanted message on live television against the backdrop of the #MeToo era so close to the midterm election.

They could also use staff lawyers to the Republican majority on the committee.

“We were told no decision has been made on this important issue, even though various senators have been dismissive of her account and should have to shoulder their responsibility to ask her questions,” the lawyers said. The lawyers said they did not know when they would have answers to the unresolved issues.

A final accord could bring to a close days of brinkmanship that have roiled Washington ahead of midterm elections and threatened to jeopardise Mr Kavanaugh’s confirmation to the court, even as some Republicans say the additional hearings may do little to change their support for him.

Earlier on Sunday, Republican Senator Lindsey Graham said lawyers for Ms Ford are contesting two Republican conditions of the proposed hearing — that Ms Ford and Mr Kavanaugh will be the only witnesses and that an independent counsel will ask the questions. “If they continue to contest those two things, there won’t be a hearing,” Mr Graham said.

I have no doubt that, if the attack on Dr. Ford was as bad as she says, charges would have been immediately filed with local Law Enforcement Authorities by either her or her loving parents. I ask that she bring those filings forward so that we can learn date, time, and place! — Donald J. Trump (@realDonaldTrump) September 21, 2018

“We’re not going to let her determine how many people we call” and on outside counsel.

“I hope she comes.”

Mr Graham, speaking on Fox News Sunday, promised a fair hearing in which both Ms Ford and Mr Kavanaugh “will be challenged” but said “unless there’s something more” to back up her accusation, then he’s “not going to ruin Judge Kavanaugh’s life over this.”

“I want to listen to her, but I’m being honest with you and everybody else, what am I supposed to do? Go ahead and ruin this guy’s life based on an accusation?” Mr Graham asked, explaining his dilemma over an allegation of a 1980s incident that is past the statute of limitations for criminal charges.

“But she should come forward. She should have her say.”

One issue that appears to have been resolved is the committee’s refusal to subpoena Mark Judge, the other person Ms Ford alleges was in the room when the assault occurred when they were high school age.

The White House is approaching Ms Ford’s potential testimony with trepidation, nervous that an emotional performance might not just damage Mr Kavanaugh’s chances but could further energise female voters to turn out against Republicans in November against the backdrop of the #MeToo movement.

Moreover, the West Wing aides who had urged Mr Trump to remain muted in his response to the accusations worried about how the president might react to an hours-long, televised hearing.

In a tweet on Friday, Mr Trump broke his silence to cast doubt on Ms Ford’s story in ways Republicans had been carefully trying to avoid.

Mr Trump mused to confidants that the “fake” attacks against his nominee were meant to undermine his presidency, according to a White House official and a Republican close to the White House. Both spoke on condition of anonymity because they were not authorised to discuss private conversations.