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

"Mike Dunleavy has been a strong and consistent Conservative since his time in the Alaska State Senate," Trump said in a statement through his Save America PAC. "I was proud to endorse his first run for Governor, and I am proud to support his reelection, too. Alaska needs Mike Dunleavy as Governor now more than ever."

Alaska Gov. Mike Dunleavy speaks at a news conference in Anchorage, Alaska, on Sept. 27, 2019. (AP Photo/Mark Thiessen)

Alaska Gov. Mike Dunleavy speaks at a news conference in Anchorage, Alaska, on Sept. 27, 2019. (AP Photo/Mark Thiessen)

Trump 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."

TARGETED BY TRUMP, ALASKA'S MURKOWSKI ANNOUNCES 2022 SENATE REELECTION CAMPAIGN

"In other words, if Mike endorses her, which is his prerogative, my endorsement of him is null and void, and of no further force or effect," Trump added.

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.

Lisa Murkowski

Sen. Lisa Murkowski, R-Alaska, asks questions during a Senate Health, Education, Labor, and Pensions Committee hearing to discuss reopening schools amid the COVID-19 pandemic at Capitol Hill in Washington, D.C., U.S., Sept. 30, 2021. (Greg Nash/Pool via REUTERS)

Murkowski announced her reelection campaign in November, but she faces an uphill battle among Republicans in the state over her handling of Trump impeachment efforts and her positions on some issues.

Earlier this year, Trump endorsed Murkowski’s GOP primary challenger, former Alaska commissioner of administration Kelly Tshibaka. Several leading members of Trump’s 2020 presidential reelection campaign are working as senior advisers on Tshibaka’s campaign, and Trump is scheduled to hold a fundraiser for her in February at his Mar-a-Lago resort in Palm Beach, Florida.

Aside from impeachment, Murkowski also ruffled Trump's feathers on other fronts. In 2017,  Murkowski voted against a Republican-backed plan to repeal Obamacare, and a year later she opposed confirmation of now-Supreme Court Justice Brett Kavanaugh, who was nominated by Trump.

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Murkowski was controversially 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 reached out to Dunleavy for comment but did not receive an immediate response.

Fox News' Paul Steinhauser contributed to this article.