Donald Trump claims Arnold Schwarzenegger was fired from the US version of the
because of poor ratings.
Schwarzenegger had said earlier that he would not be returning as host of the NBC show because of the US president.
But in an early morning tweet on Saturday Mr Trump said: "Arnold Schwarzenegger isn't voluntarily leaving the Apprentice, he was fired by his bad (pathetic) ratings, not by me. Sad end to great show."
In an interview with Empire magazine The Terminator actor said that Mr Trump's continued involvement in the show - the US president is an executive producer - had driven away viewers and sponsors.
"Even if asked (to do it again) I would decline," said Schwarzenegger. "I learned a lot, I had a great time, it was a really great opportunity. But under the circumstances, I don't want to do it again."
"With Trump being involved in the show people have a bad taste and don't want to participate as a spectator or sponsor or in any other way support the show. It's a very divisive period right now and I think the show got caught up in all that division."
The show, which wrapped up its 15th season last month, averaged fewer than 5 million viewers per episode.
Responding to Mr Trump's tweet, Schwarzenegger posted that the president should "think about hiring a new joke writer."
That was lower than any other incarnation except for a 2010 Trump-hosted edition without celebrities, and the most poorly-rated edition among the youthful viewers NBC cares most about, the Nielsen company said.
Schwarzenegger attributed the poor ratings to Mr Trump.
"It's not about the show," he said. "Because everyone I ran into came up to me and said 'I love the show ... but I turned it off as I read Trump's name I'm outta there."
Schwarzenegger added: "When people found out that Trump was still involved as executive producer and was still receiving money from the show, then half the people (started) boycotting it."
The actor and former California governor also opened up about his running feud with Mr Trump in Men's Journal. Schwarzenegger said he was tempted to "smash his (Trump's) face into the table," but instead settled on a Twitter response.
Despite still serving as executive producer, Mr Trump has more than once mocked the drop in viewership.
"Now compare him to my season 1," Trump tweeted in January. "But who cares, he supported Kasich & Hillary."
Last month, after the president pointed out the drop in Apprentice ratings during his comments at the National Prayer Breakfast, the former Republican governor responded on Twitter.
"Hey Donald, I have a great idea," Schwarzenegger said. "You take over TV, because you're such an expert in ratings, and I take over your job. And then people can finally sleep comfortable again. Hmm?"