Alaska Gov. Mike Dunleavy accepted an endorsement for reelection from former President Donald Trump, who offered his support on the condition that Dunleavy not back Alaska Sen. Lisa Murkowski in her own bid for another term.

Dunleavy said he would not endorse the Republican Murkowski, who voted to convict Trump during an impeachment trial earlier this year in response to Trump's handling of the Jan. 6 riot at the Capitol building.

"Please tell the president thank you for the endorsement," Dunleavy reportedly said. "With regard to the other issue, please tell the president he has nothing to worry about."

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Trump has endorsed Kelly Tshibaka, a former Alaska Department of Administration commissioner, who is running to replace Murkowski in 2022. Murkowski is the only Republican senator of the seven who voted to convict Trump that is running for reelection in 2022. Senate Minority Leader Mitch McConnell has endorsed Murkowski. However, the state's GOP censured Murkowski for her vote to impeach Trump.

Dunleavy, who was first elected in 2018, is running for his second term in 2022. He currently only faces Alaska state Rep. Christopher Kurka for the Republican nomination.

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"Mike Dunleavy has been a strong and consistent Conservative since his time in the Alaska State Senate. I was proud to endorse his first run for Governor, and I am proud to support his reelection, too," Trump said in his endorsement on Tuesday. "From his handling of the virus, support of the Constitution — including the Second and Tenth Amendments — taking advantage of all the opportunities Alaska has to offer, and his strong pushback against the Liberal Biden Administration's attempt to hurt our great Country."