With all precincts reporting results from Tuesday's voting, Sen. Lisa Murkowski trails her lesser-known rival Joe Miller by 1,668 votes.
But thousands of absentee ballots have yet to be counted.
The state sent out about 16,000 of them, and nearly half that many had been returned by Monday. But absentee ballots postmarked by election day can be received for up to 10 days after the election, so the count of outstanding mail-in votes won't begin for several days.
Murkowski is the daughter of former Alaska Sen. Frank Murkowski, who appointed her to the Senate when he became governor in 2002.
Miller is a West Point graduate who served in the Gulf War. He was endorsed by former Alaska Gov. Sarah Palin, conservative talk show hosts and the California-based Tea Party Express.
Palin told Fox Business Network that Alaskans "are ready for some new blood."
(Copyright 2010 by The Associated Press. All Rights Reserved.)