Senate Republicans on Tuesday stopped short of embracing Judge Roy Moore, the controversial Senate candidate who could win former Sen. Jeff Sessions' seat in December.

Moore stopped by the Senate GOP's lunch on Tuesday and was introduced to his potential Senate colleagues by Sen. John Barrasso, R-Wyo., the policy chairman.

"He was nice," said Sen. Richard Shelby, R-Ala., who supported Sen. Luther Strange, R-Ala., in the primary runoff in early September but is now backing Moore in the general election against Democrat Doug Jones. "He spoke about how he was glad to be here and had a race. He said a few words ... He was very professional."

Shelby said that no one in the lunch asked the two-time chief justice any questions during his appearance and noted that he left shortly after he spoke.

Other Senate Republicans were hesitant to say whether they'd support Moore, who holds several positions that put him at odds with many members of the Senate Republican caucus, including that Muslims should not be able to serve in the U.S. Congress and that homosexual activity should be illegal. When pressed by reporters about those comments, Moore declined to comment directly.

"I'll address that later," Moore said when asked if he believes Rep. Keith Ellison, D-Minn., a Muslim, should be able to serve in Congress.

"I'm not commenting on any issues right now," he added later on when pressed about his homosexuality stance.

After the visit, Sen. John Thune, R-S.D., the third-ranking Senate Republican, declined to say whether he will support Moore's campaign before the election to fill the remainder of Attorney General Jeff Session's Senate seat.

"Well, I'm hoping to meet with him while he's up here. I haven't had a chance to do that yet," Thune said. "I don't know him, am hoping to get to know him a little bit better, and then we'll move on from there."

Senate Republicans have been troubled by Moore's stances. Many, including Senate Majority Leader Mitch McConnell, R-Ky., supported Strange in his push for re-election that fell short.

"Well, I have trouble with those [positions]," said Sen. Orrin Hatch, R-Utah, before adding that he'll support him if he "gets duly elected."

Sen. Bob Corker, R-Tenn., said Tuesday that he will not be endorsing Moore ahead of the December 12 contest.

"I have nothing to do with his election," Corker said. "I plan on staying out of the election, and the people of Alabama will determine that. I have nothing to do whatsoever with what's happening in the Senate race in Alabama."

Since his victory in mid-September over Strange, four Senate Republicans have come out and endorsed Moore. Sens. Ted Cruz, R-Texas, Mike Lee, R-Utah, Rand Paul, R-Ky., and John Cornyn, R-Texas, who endorsed Moore last week. Cornyn is the most notable of the four given his standing as the No. 2-ranking Senate Republican and his criticisms of Moore prior to the primary runoff.

"I think just because you're a member of a political party doesn't mean you agree 100 percent," Cornyn told reporters during a press conference Monday when asked about his endorsement of Moore. "I would disagree with that statement, and I dare say if you asked each one of the members up here, what they would feel about that, they would say the same thing."

Moore is set to attend a fundraiser for his campaign on Wednesday alongside Paul former Sen. Jim DeMint. Lee was listed as a headliner for the event, but a Lee spokesman said he will not be going and "at no time ever planned to."

Moore currently holds a 6-point lead over Jones according to the latest RealClearPolitics average of polls.

Robert King contributed.