WASHINGTON – A centrist Democratic senator and two Republican colleagues argued Sunday that a decades-old sexual misconduct allegation against Judge Brett Kavanaugh should have been raised sooner in the Senate and predicted it would not prevent the chamber from moving forward with his nomination to the Supreme Court.

In televised interviews, senators Doug Jones, D-Ala., Thom Tillis, R-N.C., and John Neely Kennedy, R-La., expressed concerns that a letter outlining the allegation that Sen. Dianne Feinstein, D-Calif., received was not shared with fellow lawmakers earlier in Kavanaugh's nomination process. Kavanaugh has said he "categorically and unequivocally" denies the accusation.

The developments marked the latest chapter of a long-contentious battle over President Donald Trump's second Supreme Court nominee that has grown increasingly divisive as it approaches its final stages.

The contents of the July letter have received widespread public attention in recent news reports. The letter details an accusation from a woman who said she was at a party with Kavanaugh when they were both in high school, according to a person familiar with the matter. The alleged misconduct occurred after Kavanaugh and the woman went into a room along with a friend of Kavanaugh's, said the person, who spoke on the condition of anonymity to discuss a sensitive matter.

Feinstein, the top Democrat on the Senate Judiciary Committee, which handles Supreme Court nominations, penned an op-ed published in the Los Angeles Times on Sunday formalizing her opposition to Kavanaugh's nomination and briefly referencing her decision to share the letter's contents with the FBI.

Jones, a potentially key swing vote who has not announced whether he will support Kavanaugh's nomination, said he hopes to meet with the judge and intends to raise what he called the "very serious allegation" with him if they are able to speak.

"But at this point, it's an anonymous letter, you're not going to be able to really test it unless somebody comes forward with more information," Jones said on CNN's "State of the Union." He added, "I think that it should have been brought up, at least behind closed doors," and, "I wish someone had talked about it early on. It could maybe been cleared up."

Jones predicted that Kavanaugh's nomination would move forward, unless further information is revealed. "I just think an anonymous letter, to derail something at this late date, is just not a good practice. And I don't think it will happen," he said.

Senate Republican leaders are aiming to confirm Kavanaugh before the high court begins its fall session next month. They have given no indications the allegation will alter their plans. The Judiciary Committee plans to vote on his nomination this week, as top Republicans look to advance it to the Senate floor.

Tillis, who is a member of the Judiciary Committee, said he was "shocked" that the allegation was not raised during Kavanaugh's public or private confirmation hearings. He said he has not seen the letter and plans to seek more information about the timing of its release. Tillis said he believes Kavanaugh will win confirmation by the Senate.

"The questions that we will ask and seek answers to next week are, 'Why sit on it for weeks?' We understand that the person who wrote the letter is not willing to come forward. So we have a confidential witness not willing to sit down at least in a closed setting – that's problematic to me," Tillis said on CBS' "Face The Nation." He said he puts "some weight" on Kavanaugh's denial.

Kennedy, who also sits on the Judiciary panel, singled out Feinstein for criticism.

"Senator Feinstein's had the letter since July," he said on "Fox News Sunday." "For three months, she said nothing, nothing, zero, nada, zilch. She didn't say anything in the confirmation hearing, she didn't say anything in our confidential session with Judge Kavanaugh when the senators and nominee met privately. And now, after it's all over, she produces the letter."

The letter, which was sent to Rep. Anna G. Eshoo, D-Calif., was subsequently passed on to Feinstein, people familiar with the matter said. Other Democrats on the Judiciary Committee first learned about the contents of the letter at a last-minute meeting last Wednesday evening.

Some Democrats had privately pressed Feinstein about it as rumors about its existence began to circulate. As news reports highlighted the letter, Feinstein released a statement Thursday saying she had referred "information" about Kavanaugh to federal authorities.

In her Sunday op-ed, Feinstein accuses Kavanaugh of being overly ideological and references the sexual misconduct allegation.

"Supreme Court justices should not be an extension of the Republican Party. They must also have unquestionable character and integrity, and serious questions remain about Judge Kavanaugh in this regard, as indicated in information I referred to the FBI," Feinstein writes. "For these and other reasons detailed below, I strongly oppose Judge Kavanaugh's nomination to the Supreme Court."

Feinstein's spokesman Tom Mentzer said last week that the senator "took these allegations seriously and believed they should be public," but, "the woman in question made it clear she did not want this information to be public."

Republicans hold a 51-to-49 Senate advantage over Democrats. Many Democratic senators have declared their opposition to Kavanaugh but not a single Republican has publicly opposed him.

The two most closely-watched GOP senators are Susan Collins of Maine and Lisa Murkowski of Alaska, moderates who favor abortion rights and have broken ranks with their party in the past, including during the failed Republican effort to repeal and replace the Affordable Care Act last year. Neither has said how she plans to vote on Kavanaugh.

In addition to Jones, whose 2017 special election upset win came in a very conservative state, a trio of moderate Democrats facing re-election this year are also under a microscope. Sens. Joe Donnelly of Indiana, Heidi Heitkamp of North Dakota and Joe Manchin III of West Virginia are running in states Trump won by double-digit percentages and are under pressure to back his nominees and his agenda.

All three broke with their party last year to vote in favor of Trump's first Supreme Court nominee, now-Justice Neil Gorsuch.

The Washington Post's Felicia Sonmez and Seung Min Kim contributed to this report.