Washington (CNN) - One day after she claimed victory in the nation's last unresolved Senate race, Sen. Lisa Murkowski of Alaska reiterated Thursday that she does not support Sarah Palin as the Republican presidential nominee in 2012.
Murkowski was defeated in this year's primary by fellow Republican Joe Miller but apparently won a long shot write-in bid for the Senate seat she currently holds, finally claiming victory more than two weeks after the Nov. 2 elections. Palin, a former Alaska governor and 2008 vice presidential candidate, had backed Miller.
Palin told Barbara Walters on Wednesday she could beat President Barack Obama if she was the GOP nominee in 2012.
"She is clearly setting her sights on that higher office," Murkowski said on CNN's "American Morning" program.
"I have in the past said that Sarah Palin would not be my candidate," Murkowski added, declining to name anyone she would support.
"I'm still looking to see who will emerge in the Republican field of candidates. And I think that remains to be seen."
Murkowski also reflected on her relationship with the Republican Party, which opposed her candidacy after her defeat in the August primary.
"I was not my party's nominee," she said. "I went outside the box."
But Murkowski made it clear she remains a Republican and will continue to conference with GOP senators.
Still, Murkowski said, she was elected by a coalition of Alaskans, and "it will be all Alaskans that I will be representing."
Murkowski declared victory Wednesday, saying the result of her write-in candidacy was a "miracle."