Certified election results gave Riley a 3,117-vote lead, but Siegelman supporters have filed requests for recounts in all 67 of the state's counties.
After Pike County Circuit Judge Gary McAiley denied a request to block a recount in that county late Thursday, Riley's attorneys filed an emergency motion with the Alabama Supreme Court, asking the court to block recounts and issue guidelines for handling the election results.
The state Supreme Court, made up of eight Republicans and one Democrat, asked for written briefs early next week and scheduled oral arguments for Thursday morning in Montgomery.
"This is where it was going to end up, and for the people of Alabama, the sooner it was resolved the better," said Matt Lembke, an attorney for Riley.
"We hope, and we're confident, the Supreme Court will ratify Attorney General Bill Pryor's decision, will confirm the law of Alabama is clear and will tell canvassing board officials across this state the seals cannot be broken," Lembke said.
Meanwhile, a Tuscaloosa County circuit judge had a separate hearing Friday on whether there should be a recount in that county. And in Russell County, a court hearing on a recount is scheduled for next Friday.
Siegelman says he thinks he may gain votes from an analysis of 10,027 paper ballots in 62 counties that did not register a vote in the governor's race.
A spokesman for Siegelman's campaign, Rip Andrews, said the governor is also considering asking the state legislature to settle the election result.
"The people of Alabama are fighting for a recount in 67 counties, but Bob Riley is blocking them at every turn," Andrews said.
"The people of Alabama deserve to know who their governor is, and the only way to do that is a fair recount," he said.
Republican Dave Thomas, who conceded defeat Thursday in a secretary of state's election that was closer than the governor's race, urged Siegelman to do the same.
"None of us likes losing, but the voters have spoken and we should put an end to this sad and embarrassing challenge," said Thomas, who lost by 1,935 votes.
Riley's staff has begun interviewing candidates for posts in his administration. His transition team chairman said that applications have been received from almost 1,000 people.
Inauguration of the next governor is scheduled for Jan. 20.
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