Kevin McCarthy, former Republican US House speaker, has said that Americans should accept the results of November’s presidential race – as rising political tensions in the aftermath of Donald Trump’s campaign finance violation conviction in New York are set to inflame election integrity issues.

The relatively moderate McCarthy, who was ousted as speaker last year in a Republican power struggle and has since resigned from Congress, said on Sunday that “every American should accept the results” of the election that is expected to pit Democratic incumbent Joe Biden against the former Republican president Trump.

Related: Will Trump, a felon, be able to vote for himself in November?

McCarthy’s remarks on CNN’s Inside Politics came after Marco Rubio, the senior Florida senator and potential Trump vice-presidential pick, refused to commit to standing by the outcome on Sunday.

Like Rubio, McCarthy is an ally of Trump, and he even visited the former president after his supporters carried out the January 6 attack on the Capitol in 2021. But he is now contradicting a Republican narrative that has become a test of loyalty to Trump: questioning the integrity of the US electoral system, at least when conservative candidates lose at the ballot box.

After the guilty verdict in the New York case against Trump came down on Thursday, the Maryland Democratic congressman Jamie Raskin said that if the former president wins the vote in November then he “should be impeached before he was even sworn in” given his conviction. But other Democrats have adopted a more conciliatory position.

Hakeem Jeffries, the Democratic House minority leader, said Sunday that he would “certainly” accept the results “because in America the peaceful transfer of power is sacrosanct”.

Jeffries cast the blame on the extreme right wing of the Republican party, saying that “many Americans – Democrats, independents and traditional Republicans – have been troubled by the election denialism or the denial that we’ve seen coming from the other side of the aisle”.

Trump has also said that he would accept November’s vote – but only, he told the Milwaukee Journal Sentinel in May, “if everything’s honest”.

On Sunday night, Trump posted on his social media site that he planned to appeal his conviction in New York to the supreme court ahead of his scheduled sentencing on 11 July.

McCarthy, who is free of political obligation to Trump, had previously signed a legal petition soon after the 2020 election that urged the supreme court to review a Texas lawsuit challenging the election results in several swing states.

He also voted not to certify election results from Arizona and Pennsylvania during the vote certification process that came after police managed to halt the 2021 Capitol attack.

But in his interview with CNN, McCarthy said that resistance to election results was not just a question for politicians but “for the whole American public”.

“We’ve gotta get beyond it,” McCarthy said.