The South Dakota lawmaker told Fox that he would "welcome" the ex-President's help to win back his party's control of Congress in the forthcoming midterms -- but added that debating the conspiracy theory over the presidential race could set them back.
Hours later Trump landed in Arizona to hold his first rally of the year, where he again published his grievances about November 2020.
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Thune is the No. 2 Republican senator behind Minority Leader Mitch McConnell and is generally seen as his probable heir to lead the Senate GOP.
"To the degree that President Trump can be helpful, can contribute to" winning back the Senate majority, "we welcome that," Thune said.
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"But I think any time we're talking about the 2020 election and rehashing that, it takes our eyes off the ultimate prize."
He claimed the key to good election was moving forward -- making an inconspicuous rebuke aimed at Trump and his Congressional allies still fighting a two-year squabble over who won the White House.
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"I think most Republican senators understand that, in order for us to be successful as a country, that we have to get the majority back in the Senate, and that means focusing on the future not the past," Thune said.
"We welcome the former president's support of that, but would hope that he would play a constructive role and contribute to helping us win the majority back in 2022."
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McConnell's deputy admitted that Trump still "attempts" to sway the Republican Party, but his election fraud complaints come second to the Senate GOP's priority of holding Biden accountable.
"President Trump still has a tremendous following among our supporters across the country and, you know, exercises that influence, or at least attempts to, on a daily basis," Thune said.
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"But I think ultimately for us as Republican senators our job right now is to try to get the majority back in 2022 and provide that check and balance against this crazy Biden administration agenda."
Trump spoke in Florence, Arizona, where he told a charged-up crowd that the state "got taken away" from him in the last presidential race.
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He lost the Grand Canyon state to Biden by a thin margin of 49.4 percent to 49.1 percent.
"Last year we had a rigged election and the proof is all over the place," the former President said.
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