U.S. Sen. Michael Bennet said Monday that the confirmation process for U.S. Supreme Court nominee Brett Kavanaugh should be paused until the FBI has investigated allegations of sexual misconduct that have emerged in the last week, including new claims made by a Boulder woman who says Kavanaugh exposed himself to her when they were college students.

Bennet’s demand came after Senate Majority Leader Mitch McConnell, a Kentucky Republican, blasted Democrats on the Senate floor Monday, accusing them of waging a “smear campaign” against Kavanaugh and calling the latest allegation “another orchestrated, last-minute hit on the nominee.”

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McConnell vowed that senators will vote on Kavanaugh’s nomination to the high court “in the near future.”

Bennet, a Colorado Democrat, said last week that he’s decided to vote against Kavanaugh, if the nomination makes it to the full Senate.

As Colorado Politics reported Sunday, Deborah Ramirez, a 53-year-old Boulder woman who attended Yale University with Kavanaugh, told The New Yorker that he pulled down his pants and thrust his penis in her face at an alochol-fueled dorm party in the early 1980s.

The new allegations emerged just hours after the Senate Judiciary Committee scheduled an extraordinary hearing Thursday to hear from Kavanaugh and Christine Blasey Ford, a California woman who says he sexually assaulted her in Maryland when both were teenagers.

Kavanaugh has roundly denied the allegations, denouncing the women for leveling “smears, pure and simple.”

> RELATED: Trump fires back against Colo. woman’s accusation against Kavanaugh

In a tweet posted Monday afternoon, Bennet said: “Both Dr. Ford & Ms. Ramirez have said they are willing to provide their accounts to the FBI under oath. Anyone who is disputing their accounts should also be willing to do so under oath. The nomination process should not move forward until the FBI investigates these allegations.”

Both Dr. Ford & Ms. Ramirez have said they are willing to provide their accounts to the FBI under oath. Anyone who is disputing their accounts should also be willing to do so under oath. The nomination process should not move forward until the FBI investigates these allegations.

— Michael Bennet (@SenatorBennet) September 24, 2018

Bennet’s Colorado colleague, Republican U.S. Sen. Cory Gardner, said earlier Monday he supports an investigation into the new allegations by the judiciary committee’s GOP-controlled staff, but he stopped short of calling for the FBI to look into the charges.

A spokesman for Gardner didn’t respond to an inquiry seeking clarification.

Meanwhile, Senate Democratic leader Chuck Schumer of New York argued Monday that a “quiet, serious and thorough” FBI background check would be the best way to resolve the raging controversy over Kavanaugh’s confirmation. He added that GOP senators should welcome the probe, if they really believe the allegations are part of a “smear campaign.”

– The Associated Press contributed to this report