Florida governor Ron DeSantis has pointedly refused to join his Republican rival Vivek Ramaswamy in boycotting next year's presidential election in Colorado.
Mr Ramaswamy, who is vying with Mr DeSantis for the GOP nomination in 2024, suggested on Wednesday that candidates should withdraw from the ballot unless Donald Trump is also allowed to run.
One day earlier, the Colorado Supreme Court had disqualified Mr Trump from seeking office because his efforts to overturn the 2020 election result had constituted an "insurrection".
"I pledge to withdraw from the Colorado GOP primary ballot unless and until Trump’s name is restored," Mr Ramaswamy said in a video posted on X, formerly known as Twitter. He also "demanded" that other Republicans should do the same.
Asked by the conservative broadcaster Newsmax on Wednesday whether he would follow suit, Mr DeSantis said: "No, I think that's just playing into the Left."
He added: "I think the case will get overturned by the [US] Supreme Court.
"I've qualified for all the ballots, I'm competing in all the states, and I'm going to accumulate the delegates necessary. That's the whole name of the game in this situation.
"But I do anticipate that that decision was political and will get reversed."
The 14th Amendment to the US constitution, adopted in 1868 in the wake of the US Civil War, forbids any candidate from holding office if they have "engaged in an insurrection".
Four out of seven Colorado justices agreed that Mr Trump had met this standard by inciting his followers to invade the Capitol on 6 January 2021 and continuing to support their efforts even as the day turned violent.
Mr Trump has vowed to appeal the ruling, and it may yet be overturned by the US Supreme Court, which has an overwhelming conservative majority.