Arnold Schwarzenegger has ruled out a run for the US Senate, in response to widespread speculation that the actor would return to political life to take on Donald Trump.

Schwarzenegger, who was governor of California from 2003 to 2011, had been tipped by political insiders to enter the 2018 race for the US Senate, either as a Republican or an independent, in a move that would have given him a public platform to oppose Trump’s presidency. However, Schwarzenegger refuted the rumours in a Facebook post published on Sunday, suggesting instead that he would continue his battle against political gerrymandering.

“I’m deeply flattered by all of the people who have approached me about running for Senate, but my mission right now is to bring sanity to Washington through redistricting reform like we passed here in California,” he wrote. “Gerrymandering has completely broken our political system and I believe my best platform to help repair it is from the outside, by campaigning for independent redistricting commissions.

“Thank you for your kind messages and all of the support and I hope you’ll join me in my battle against gerrymandering with the same enthusiasm.”

Schwarzenegger has long been a vocal critic of Trump, supporting Trump’s opponent John Kasich in the Republican primaries and later announcing that he wouldn’t vote for Trump as president, following the release of a widely condemned recording in which Trump boasted about groping women. It was the first time that Schwarzenegger had not voted for a Republican candidate for president since he became a US citizen in 1983.

A Twitter feud between the pair has intensified in the weeks following Trump’s swearing in as president. Trump mocked the ratings of his successor as host of The Celebrity Apprentice, at the National Prayer Breakfast in February, and Schwarzenegger suggested in response that the two men should swap jobs, so that “people can finally sleep comfortably again”.

Earlier this month, Schwarzenegger announced that he would not return as host of The New Celebrity Apprentice, blaming Trump’s continued involvement in the show, as executive producer, for its poor ratings. Trump in turn claimed in a tweet that Schwarzenegger had not resigned but had been “fired by his bad (pathetic) ratings.... Sad end to great show”.