Sen. Lisa Murkowski claimed victory in her historic write-in bid for the U.S. Senate Wednesday night, thanking Alaskans and telling cheering supporters: "I think we can say our miracle is here."

Unprecedented in modern politics, the win returns the Republican incumbent to Washington, D.C., in a drawn-out defeat of tea party-backed conservative Joe Miller.

The Associated Press and the state Republican Party called the race for Murkowski on Wednesday, with the Alaska GOP asking Miller to stand down. "We call on Joe Miller to respect the will of the voters and end his campaign in a dignified manner," chairman Randy Ruedrich said in a prepared statement.

But the Fairbanks Republican -- who staggered the Murkowski camp by winning the party primary in August -- said he's not conceding.

The Miller camp has called the state voting system "suspect." It's challenging the count in court and says the state Division of Elections has not complied with its request to review "voting tapes" from the ballot machines that record the votes cast.

"It's not that we believe necessarily that we're going to come out on top," Miller said in a phone interview. Instead, he said, the campaign wants to make sure the counting process is a fair one.

Asked if he sees any scenario in which he could still win, he said: "I don't think it's impossible."

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