Sen. Lisa MurkowskiLisa Ann MurkowskiEmboldened Trump takes aim at GOP foes The Hill's 12:30 Report - Presented by Facebook - DC prepares for Saturday of festivals & Jan. 6 demonstration Republican leaders misjudged Jan. 6 committee MORE (R-Alaska) said on Monday that President TrumpDonald TrumpKinzinger says Trump 'winning' because so many Republicans 'have remained silent' Our remote warfare counterterrorism strategy is more risk than reward Far-right rally draws small crowd, large police presence at Capitol MORE should concede the White House race to President-elect Joe BidenJoe BidenSunday shows preview: Coronavirus dominates as country struggles with delta variant Did President Biden institute a vaccine mandate for only half the nation's teachers? Democrats lean into vaccine mandates ahead of midterms MORE.
"I think he should concede. I think the race is over," Murkowski told CNN.
Spokespeople for Murkowski didn't immediately respond to a question about her remarks. Murkowski, who didn't vote for Trump in 2016, has not disclosed if she voted for him in the 2020 presidential election earlier this month.
Murkowski previously released a statement saying that it was "time to begin the full and formal transition process."
She also rebuked a "pressure campaign on state legislators" as "inconsistent with our democratic process."
But her remarks on Monday are among the most direct calls from Senate Republicans for Trump to formally bow out of the White House race weeks after media organizations projected Biden as the winner. Trump has launched myriad unsuccessful legal attempts in key states, which have begun certifying Biden's victory.
Though a growing number of GOP senators have recognized that Biden will be sworn in on Jan. 20 and many have called for the transition process to begin, most have not called on Trump to formally concede the race.
Sen. Bill CassidyBill CassidySunday shows preview: Coronavirus dominates as country struggles with delta variant GOP senator on Texas abortion law: Supreme Court will 'swat it away' when 'it comes to them in an appropriate manner' GOP hopes spending traps derail Biden agenda MORE (R-La.), in a pair of tweets earlier this month, said that Trump's legal team "has not presented evidence of the massive fraud which would have had to be present to overturn the election."
"The transition should begin for the sake of the country," he added, noting that Biden had "won" the election.
Sen. Lamar AlexanderLamar AlexanderAuthorities link ex-Tennessee governor to killing of Jimmy Hoffa associate The Republicans' deep dive into nativism Senate GOP faces retirement brain drain MORE (R-Tenn.), in a statement last week, also called for Trump to "take pride in his considerable accomplishments, put the country first and have a prompt and orderly transition to help the new administration succeed."
But Trump has shown no signs of backing down. In tweets over the weekend, he referred to the "election hoax" and repeated his baseless claim that the White House race was "rigged."
Top Republicans on Monday brushed off questions about the president's rhetoric, noting that the administration had signed off on letting the transition process move forward.
"Well, I mean, I think the important thing for us is the transition's moving forward, and he has authorized that, which I think suggests at least that he understands where this is headed. I don't think anybody probably expected that he was going to follow past conventions when it comes to anything. This has not been a conventional presidency," said Sen. John ThuneJohn Randolph ThuneManchin keeps Washington guessing on what he wants Manchin-McConnell meet amid new voting rights push Republican leaders misjudged Jan. 6 committee MORE (S.D.), the No. 2 Senate Republican.
Asked if he considered Biden to be president-elect, he added, "The trajectory is in that direction for sure."