Election officials said thousands of additional absentee and write-in ballots indicated Murkowski won 92,164 write-in votes to Miller's 90,448 votes as of late Monday, Politico reported.
Miller's campaign had challenged 7,601 write-in votes that election officials ultimately counted for Murkowski, who mounted her write-in campaign after losing to the Tea Party-backed Miller in the Republican Party primary.
Murkowski's campaign said it expects her lead to increase in the next few days as more write-in ballots are opened and counted. So far, Murkowski won 89.3 percent of the write-in votes outright with at least 8,500 more write-in ballots to be counted.
Murkowski campaign manager Kevin Sweeney said in a statement Monday if Murkowski maintains her edge in write-in votes, she could win the election outright without considering the ballots challenged by Miller.
When that occurs, Sweeney said, the Murkowski camp expect Miller "to concede this race, as he has indicated he would."
Miller's campaign was expecting a bump Monday when officials counted thousands of absentee ballots, which tilted in his favor in both the primary and the general election so far, Politico said. State election officials said they counted about 8,700 absentee ballots Monday, less than planned, and are scheduled to open thousands more absentee ballots this week.
Observers said it would be nearly impossible for Miller to win without a legal challenge of ballots already counted for Murkowski, Politico said.
Miller filed a lawsuit last week, arguing that voters must spell Murkowski's name correctly for their write-in ballots to count. A federal judge is expected to hear arguments this week.