Miller is appealing a state judge's decision to toss out his challenge to the handling of the election and counting of write-in ballots for Murkowski, who waged a write-in campaign after losing the GOP primary to Miller.

The state Supreme Court did not immediately rule Friday.

Miller wants the results of the election invalidated, and a recount to ensure what he has called a fair and accurate tally.

He watched Friday as his attorney, Michael Morley, told the court the state should be held to a strict reading of a law that calls for ovals on ballots to be filled in, and for the last name of a candidate or the name as it appears on the declaration of candidacy to be written.

The state, relying on case law, allowed for ballots with misspellings to be counted toward Murkowski's tally and used discretion in determining voter intent.

Murkowski attorney Scott Kendall told the high court Miller is "denying reality" in continuing in his legal challenge. But justices, particularly Daniel Winfree, grilled Kendall about his belief the case is moot, noting that there hasn't been a recount or a re-evaluation of challenged ballots that might add to Miller's tally.