Several Republican senators said Thursday that Alabama Senate candidate Roy Moore should abandon the race if reports are true that he sexually pursued teenage girls when he was in his 30s.

"If these allegations are true, he must step aside," McConnell said. He also called the reports "very disturbing."

McConnell was seen on the Senate floor Thursday afternoon talking to Alabama's incumbent Sen. Luther Strange, who Moore defeated in the GOP primary. McConnell, President Trump and many other Republicans backed Strange, and it's possible the GOP will be looking for Strange to run as a write-in.

The Washington Post reported Moore engaged in sexual contact with a 14-year-old girl when he was 32 years old and a powerful attorney in a small Alabama town, which included an on-the-record interview with the woman, Leigh Corfman.

LIST: All the Republicans calling for Roy Moore to step down after allegations he pursued 14-year-old girl

Corfman said she did not have sex with Moore, who at the time was an assistant district attorney, but that “I wanted it over with — I wanted out,” and that she thought, “Please just get this over with. Whatever this is, just get it over.”

Three other women told the Post that when they were between 16 and 18 years old and Moore was in his 30s. Each of the women was quoted by name, though none alleged sexual contact during the alleged incidents, which occurred between 1979 and 1982.

Senate Majority Whip John Cornyn, R-Texas, was one of the first high profile Republican senators to endorse Moore, and wouldn't call for the Alabama challenger to step aside just yet.

“I find the story to be deeply troubling,” Cornyn said. He added that he wants Alabama Gov. Kay Ivey and the Alabama voters on what the "immediate next steps" should be.

Cornyn later added he doesn't think Moore's candidacy should continue if the allegations are proven accurate.

"If it is true I don't think his candidacy is sustainable. But we believe in a presumption of innocence until proven guilty so I think it's important for the facts to come out," Cornyn said, adding, "I'm interested in seeing what the substantiation is for the story."

Related: Alabama state auditor defends Roy Moore against sexual allegations, invokes Mary and Joseph

Utah Sen. Mike Lee, another Republican senator who had endorsed Moore, said he should "resign" if the allegations are true.

“If these allegations are true, Judge Moore should resign," Lee said.

Arizona Sen. John McCain was the only Republican senator to call for Moore to step aside without the qualification of finding out if the allegations are true.

“The allegations against Roy Moore are deeply disturbing and disqualifying," McCain said. "He should immediately step aside and allow the people of Alabama to elect a candidate they can be proud of.”

Other Republican senators were quick to call for Moore to step aside with the caveat of finding out if the allegations are true.

Sen. Richard Shelby, who would be Moore's fellow Alabama senator, said he shouldn't be in the upper chamber if the report is accurate.

"If that's true, he wouldn't belong in the Senate," Shelby said.

"The allegations against Alabama Senate candidate Roy Moore are deeply troubling," National Republican Senate Committee Chairman Cory Gardner said. "If these allegations are found to be true, Roy Moore must drop out of the Alabama special Senate election."

"If they are true then he should seriously think about stepping aside," said Sen. Mike Rounds, R-S.D. "Always when someone is accused of that it is concerning to us."

Sen. Tim Scott, R-S.C., and Sen. Thom Tillis, R-N.C., felt the same way.

"If they're accurate, he should step aside," Scott said.

"If they're proven to be true, he should step aside," Tillis added.

Maine Sen. Susan Collins added her own condemnation of Moore's alleged actions on Twitter.

"If there is any truth at all to these horrific allegations, Roy Moore should immediately step aside as a Senate candidate," she said.

Only five Republicans have formally endorsed Moore's campaign against Democrat Doug Jones: Sens. Ted Cruz, R-Texas, Rand Paul, R-Ky., Steve Daines, Lee, and Cornyn.

Reporter Laura Barron-Lopez contributed to this story.