Sen. Susan Collins (R-ME) speaks to reporters as she arrives for a nomination vote on Capitol Hill in Washington, December 13, 2017.

"Obviously if Judge Kavanaugh has lied about what happened that would be disqualifying," Collins said during a brief gaggle with the press outside her office.

Sen. Susan Collins , R-Maine, told reporters on Monday that if Supreme Court nominee Brett Kavanaugh lied in denying that he sexually assaulted a woman at a high school party in the early 1980s that it would "obviously" disqualify him from a seat on the nation's highest court.

Kavanaugh has vigorously denied that the alleged incident ever took place, and a White House official told NBC News Monday that Kavanaugh has said that he was not at the party. Kavanaugh gave the same account to Sen. Orrin Hatch, R-Utah, a Hatch aide told NBC News.

Collins also continued to demand a hearing on the issue with Kavanaugh and his accuser, Christine Blasey Ford, a position which seemingly puts her at odds with GOP leadership. Collins' first demanded a hearing, with both parties under oath, in a tweet earlier Monday.

Collins tweet

Sen. Lisa Murkowski, R-Alaska, who is also viewed as a potential swing vote in Kavanaugh's candidacy, voiced her support for a hearing, as well.

"Allegations surrounding sexual assault must be taken seriously and the Judiciary Committee must look into this further," Murkowski told CNBC in a statement Monday evening.

"Despite the length of time since the alleged incident, Dr. Ford's allegations should be heard and she must have an opportunity to present her story before the committee under oath, with Judge Kavanaugh having the opportunity to respond under oath as well," Murkowski added.

Judiciary Committee Chairman Chuck Grassley, R-Iowa, has proposed holding phone calls with Kavanaugh and Ford, a plan which Senate Majority Leader Mitch McConnell, R-Ky., endorsed Monday from the Senate floor.

Collins said Monday that she assumed staff interviews "would be the prelude to some sort of hearing."

She said that during a phone call with Kavanaugh Friday, after the contours of the accusation against him were public but before Ford came forward by name, the nominee told her "that he had never acted that way not only with this unnamed accuser but with any woman."