Superior Court Judge William Carey last week ruled Miller, a Tea Party-supported Republican, offered no evidence to support his claim of election fraud, and said election officials used the correct standard when they accepted ballots where Murkowski's name was misspelled but a write-in vote for her was clearly intended.
Murkowski, a Republican, mounted a write-in campaign as an independent after Miller bested her in the party primary.
Oral arguments are scheduled for Friday, KTUU-TV, Anchorage, reported. Miller filed his appeal Monday.
"We have consistently asserted that the law should be followed strictly," Miller said in a statement posted on his Web site. "The fact that the Legislature stated that there should be 'no exceptions' to the ballot counting method is what, in our view, should govern this matter. Under the current ruling, there are now over 8,000 exceptions, a result everyone who favors the rule of law should question."
Miller said portions of Carey's ruling "essentially modifies" state law that requires write-in ballots to match the candidate's declaration form. He said Carey's ruling would permit questionable ballots to be counted as long as an election official determines voter intent.
If Miller hadn't appealed by Monday, a federal stay on certifying the election results would have been lifted and the state would have certified Murkowski's victory, a state official said.
"The timeline would go this way: If the federal court allows us to certify and the state Supreme Court holds the Superior Court decision, then the election would be certified," Alaska Lt. Gov. Mead Treadwell said. However, "That does not mean that Mr. Miller can't then ask for a recount."