Alaska voters Tuesday selected former state attorney general and Natural Resources commissioner Dan Sullivan as the Republican nominee in this fall's U.S. Senate race against Democratic incumbent Sen. Mark Begich.

With 98.6 percent of precincts reporting Wednesday morning, Sullivan led by more than 7,000 votes over his nearest challenger, tea party favorite Joe Miller, with Alaska Lt. Gov. Mead Treadwell down by more than 13,000 votes. Sullivan's support equated to 40 percent of the vote, while Miller had 32 percent and Treadwell had 25 percent.

At least 14,581 votes remain to be counted in the election, Division of Elections Director Fenumiai said.

Sullivan did not speak Tuesday night; his campaign said he was waiting for a national media outlet to call the race. Shortly after 1:30 a.m., his campaign released a statement declaring victory and quoting Sullivan as saying: "Our success was about Alaskans coming together to decide the direction we take our state."

Treadwell conceded late Tuesday, and Miller's campaign issued its own statement early Wednesday morning congratulating Sullivan.

By 8 a.m. Wednesday, two of the independent groups that supported Begich and Sullivan during the primary campaign had already released new negative television ads targeting their opponents.

Washington, D.C.-based Crossroads G.P.S., a Republican group co-founded by Karl Rove, is attacking Begich for what it says is a pay differential between his male and female staff members in a commercial starting on television Wednesday.

Anchorage-based Put Alaska First, a pro-Begich group that's raised the vast majority of its money from a Washington, D.C., political committee tied to Democratic Senate Majority Leader Harry Reid, has its own commercial starting Thursday that attacks Sullivan for his support for the Pebble Mine project in southwest Alaska.

The commercial was released on YouTube on Wednesday.

Begich officially kicks off his general election campaign with a speech at a downtown Anchorage hotel at noon Wednesday.

This is a developing story. Check back for updates.