An Alaska judge Friday evening rejected a challenge by Senate candidate Joe Miller (R) to the election results that appear to have returned Sen. Lisa Murkowski (R) to the Senate.

Miller, who trails by more than 10,000 votes in the still-unresolved contest, has argued that Murkowski should not be certified the winner because of concerns about ballots cast in her remarkable write-in campaign for re-election. In the GOP primary, Miller had beaten Murkowski with the support of tea party activists and former Gov. Sarah Palin (R), but Murkowski ran as a write-in candidate in the general election.

Miller has complained that the results were tarnished by misconduct by election officials and questions about the intent of voters writing in Murkowski’s name. 

Superior Court Judge William Carey rejected Miller’s arguments Friday, leaving him until Tuesday to file an appeal.

“On November 17, 2010, Miller received notice of fraud allegations by his observers,” the judge wrote.

“From November 17 to December 2, 2010, Miller had time to contact officials and at least attempt to provide sufficient evidence to overcome both the presumption election officials did not act legally but also to show malconduct which would sufficiently change the election. He did neither.”

The Anchorage Daily News quoted a Miller spokesman Friday evening as saying that an appeal to the state Supreme Court is “under advisement.”