Senate Minority Leader Mitch McConnell (Ky.) is offering his full support to Alaska GOP Senate nominee Joe Miller, and is urging his fellow Republicans to do the same, even though Senate GOP Conference Vice Chairwoman Lisa Murkowski is still pondering a general election bid as a write-in candidate.

McConnell has already donated $10,000 to Miller, the Fairbanks attorney who defeated Alaska’s senior Senator in last month’s Republican primary, and he is now recommending that Senate Republicans support the GOP nominee over their vanquished colleague.

“When Joe Miller earned the votes of Republican primary voters in Alaska he earned my full support for his campaign to represent Alaskans in the U.S. Senate,” McConnell said in a prepared statement released by the Miller campaign late Thursday. “Washington sorely needs to stop the massive government expansion that is drowning our children and grandchildren in debt. When Joe wins this November I know I can count on him to help lead this fight.”

At McConnell’s urging, Republican Senators are planning to hold fundraising events for Miller, with McConnell also recommending that fellow Republicans donate to Miller’s campaign. Miller has also received strong endorsements from Sen. John McCain (R-Ariz.) and National Republican Senatorial Committee Chairman John Cornyn (Texas).

The NRSC this week donated $42,600 to Miller’s campaign, and has promised him another $170,000 in coordinated funds.

Murkowski narrowly lost her primary to Miller, and is considering ways to remain in the Senate race. Running as a write-in appears to be the most likely scenario, but she stands to lose her Conference leadership position and her ranking slot on the Energy and Natural Resources Committee even if she were to prevail on Nov. 2.