Arnold Schwarzenegger said on Friday that he will not return as host of The New Celebrity Apprentice, and blamed Donald Trump for the reality show’s recent poor performance.

On Saturday, in response, Trump followed a series of tweets that alleged President Obama had his offices wire-tapped with a barb at Schwarzenegger, who he said had been “fired by his bad (pathetic) ratings”.

Speaking to the Empire website, the former California governor said he would not mind working with NBC and producer Mark Burnett again, “on a show that doesn’t have this baggage”.

Schwarzenegger replaced the president as host of the show, but Trump remained as an executive producer. The president taunted Schwarzenegger for the show’s recent poor performance in the ratings, even mocking him during an address at the National Prayer Breakfast.

The show, which wrapped up its 15th season last month, averaged fewer than five million viewers per episode. That was lower than any other incarnation except for a 2010 Trump-hosted edition without celebrities. It was also the most poorly rated edition of the show among the youthful viewers NBC cares most about, the Nielsen company said.

Even if he were asked to host the show again, Schwarzenegger said, he wouldn’t want to do it.

“With Trump being involved in the show people have a bad taste and don’t want to participate as a spectator or as a sponsor or in any other way support the show,” he told Empire. “It’s a very divisive period now and I think this show got caught up in all that division.”

On Saturday, Trump wrote: “Arnold Schwarzenegger isn’t voluntarily leaving the Apprentice, he was fired by his bad (pathetic) ratings, not by me. Sad end to great show.”

After Schwarzenegger’s debut in January, Trump wrote on Twitter that the show had been swamped “in comparison to the ratings machine, DJT”.

Schwarzenegger shot back, saying on social media that he hoped Trump would work for the American people as aggressively as he did for his ratings. The actor, like Trump a Republican, did not endorse Trump for president and said he would not vote for him.

When The New Celebrity Apprentice ended its season last month, Trump tweeted that Schwarzenegger “did a really bad job as governor of California and even worse on The Apprentice, but at least he tried hard”.

NBC had no immediate comment about whether the show would return with a new host.