Alaska Sen. Lisa Murkowski said she could not support Sarah Palin (R) if her state's former governor were to run for president.

Murkowski, a senior Republican in the Senate who's waging a write-in candidacy for reelection, rejected supporting Palin, who worked to defeat Murkowski this fall. 

"If she were to run right now, I would not support her as president," Murkowski said during a debate Wednesday night.

The senator made those comments during a debate against Democrat Scott McAdams and Joe Miller, the Republican nominee who bested Murkowski in the primary with Palin's backing.

Bad blood between Palin and Murkowski already existed before the primary fight. Palin defeated the senator's father, Gov. Frank Murkowski, in a Republican primary challenge in 2006, a win that started Palin's political path.

Murkowski's formal rejection of Palin seems significant considering new polling showing the incumbent leading the three-way field in the closing days of the campaign.

Thirty-four percent of Alaska voters said they prefer to support a "write-in candidate" — broadly construed to mean Murkowski — in Tuesday's election, according to a Hays Research Group poll released Thursday. McAdams would get 29 percent of the vote if the election were held today, while 23 percent would vote for Miller. (The poll, conducted Oct. 26, has a 4.8 percent margin of error.)

Aiding Murkowski's candidacy was a ruling Wednesday evening by the state Supreme Court that allowed elections officials to provide voters with a list of write-in candidates. This would ostensibly provide voters with a reminder of — and correct spelling of — Murkowski's name and lessen the chances of voter errors that would disqualify votes for Murkowski.

Republican leaders have backed Miller in the race, and Palin will lead a rally in Alaska on Thursday featuring other Republican leaders — such as Sen. Jim DeMint (S.C.) and Rep. Michele Bachmann (Minn.) — to bolster his candidacy.

Murkowski has said that if she's reelected, she intends to consider herself a Republican for purposes of caucusing.

Updated 9:03 a.m.