Alaska Gov. Mike Dunleavy accepts Trump's conditional endorsement that targeted Murkowski

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Republicans in Alaska are giving each other the cold shoulder.

Gov. Mike Dunleavy of Alaska accepted former President Donald Trump's endorsement, which came with the stipulation that he does not endorse Republican Sen. Lisa Murkowski. The Alaskan senator has repeatedly rebuked Trump's influence in the party, and voted to impeach the former president after the Jan. 6 Capitol riot.

"Lisa Murkowski is the ‘disaster from Alaska’ who single-handedly blew ANWR, one of the largest energy sites in the world, and an incredible economic development opportunity for the Great State of Alaska!" the memo stated.

TRUMP ENDORSES ALASKA GOV. DUNLEAVY FOR REELECTION -- AS LONG AS HE DOESN'T BACK SEN. MURKOWSKI

"This is why Mike Dunleavy of Alaska has been, and will be, a great Governor. He has the courage of his convictions," the memo also read.

UNITED STATES - March 4: Sen. Lisa Murkowski, R-Alaska, speaks during the Senate Energy and Natural Resources Committee business meeting to vote on sending the nomination of Rep. Deb Haaland, D-N.M., to be Interior Secretary, to the Senate floor in Washington on Thursday, March 4, 2021. (Photo by Caroline Brehman/CQ-Roll Call, Inc via Getty Images)

Former President Donald Trump announced Tuesday his support for the reelection bid by Alaska Republican Gov. Mike Dunleavy. However, Trump made clear his endorsement hinges on whether the governor backs one of Trump's most vocal Republican critics in the Senate.

Trump previously said Dunleavy has his "Complete and Total Endorsement" but stated that the endorsement is "subject to his non-endorsement of Senator Lisa Murkowski who has been very bad for Alaska, including losing ANWAR, perhaps the most important drilling site in the world, and much else."

Dunleavy thanked Trump for the endorsement in a note to Trump. In the note, the governor thanked Trump for all he "has done for Alaska."

FILE - In this Sept. 27, 2019, file photo, Alaska Gov. Mike Dunleavy speaks at a news conference in Anchorage, Alaska. (AP Photo/Mark Thiessen)

"Please tell the President thank you for the endorsement," Dunleavy wrote. "With regard to the other issue, please tell the President he has nothing to worry about. I appreciate all 45 has done for Alaska and this country."

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Murkowski, a moderate Republican with a history of working across the aisle to achieve bipartisan agreements, was one of seven Senate Republicans to vote to convict the former president in his February impeachment trial. She is now the only one of those seven running for reelection in the 2022 midterm elections.

Murkowski was appointed to the U.S. Senate in late 2002 by her father, Frank, who had just resigned from his Senate seat after being elected governor.

Fox News' Kyle Morris contributed to this report.