Alaska Administration Commissioner Kelly Tshibaka announced her Senate campaign with a vow to defeat Murkowski, who has been in the Senate since 2002 but has not yet announced formal plans to seek re-election next year.
"I'M IN!" Tshibaka said on Twitter. "I am running for the Senate to represent our conservative Alaska values. We're going to defeat Lisa Murkowski and show the DC insiders what happens when Alaska has strong conservative leadership!"
A Murkowski spokeswoman was not immediately available for comment.
Murkowski, 63, who was appointed to the Senate in 2002, has been elected three times, including once in 2010 after she lost her Republican primary to a Tea Party candidate but mounted a successful write-in campaign in that year's general election. Tshibaka's announcement made no mention of Trump but came less than a month after the former president vowed to campaign against Murkowski, calling her a "failed candidate" and a "disloyal and very bad senator."
A Trump critic, Murkowski was one of seven Republicans who voted to convict him at his Senate impeachment trial last month.