"I think we can say our miracle is here," the Republican incumbent told supporters as she claimed victory in her historic write-in victory, 15 days after the midterm election.
Murkowski's victory over her Tea Party challenger makes her the first write-in candidate to win a seat in the U.S. Senate since Strom Thurmond achieved the feat in 1954 in South Carolina.
Miller's campaign has requested a statewide hand recount of all votes, the Anchorage Daily News reported.
"Given how close the vote totals are, Miller needs to be given the same opportunity of having all of his ballots inspected and counted by hand to ensure every vote cast for him is counted," Miller campaign spokesman Randy DeSoto said Tuesday.
However, Division of Elections Director Gail Fenumiai told the newspaper in an e-mail Alaska does not conduct thorough hand recounts.
"Recounts are done using the optical scan equipment," she said.
Miller -- who was endorsed by former Alaska Gov. Sarah Palin -- has already filed two lawsuits and the decision not to recount votes by hand could lead to a third, the Daily News said.