Apple on Thursday rejected Elon Musk's claim that its digital App Store favors OpenAI's ChatGPT over his company's Grok and other rival AI assistants.

Musk has accused Apple of giving unfair preference to ChatGPT on its App Store and threatened legal action, triggering a fiery exchange with OpenAI CEO Sam Altman this week.

"The App Store is designed to be fair and free of bias," Apple said in reply to an AFP inquiry.

"We feature thousands of apps through charts, algorithmic recommendations, and curated lists selected by experts using objective criteria."

Apple added that its goal at the App Store is to offer "safe discovery" for users and opportunities for developers to get their creations noticed.

But earlier this week, Musk said Apple was "behaving in a manner that makes it impossible for any AI company besides OpenAI to reach #1 in the App Store, which is an unequivocal antitrust violation," without providing evidence to back his claim.

"xAI will take immediate legal action," he said on his social media network X, referring to his own artificial intelligence company, which is responsible for Grok.

X users responded by pointing out that China's DeepSeek AI hit the top spot in the App Store early this year, and Perplexity AI recently ranked number one in the App Store in India.

DeepSeek and Perplexity compete with OpenAI and Musk's startup xAI.

Altman called Musk's accusation "remarkable" in a response on X, charging that Musk himself is said to "manipulate X to benefit himself and his own companies and harm his competitors and people he doesn't like."

Musk called Altman a "liar" in the heated exchange.

OpenAI and xAI recently released new versions of ChatGPT and Grok.

App Store rankings listed ChatGPT as the top free app for iPhones on Thursday, with Grok in seventh place.

Factors going into App Store rankings include user engagement, reviews and the number of downloads.

Grok was temporarily suspended on Monday in the latest controversy surrounding the chatbot.

No official explanation was provided for the suspension, which followed multiple accusations of misinformation including the bot's misidentification of war-related images — such as a false claim that an AFP photo of a starving child in Gaza was taken in Yemen years earlier.

Last month, Grok triggered an online storm after inserting antisemitic comments into answers without prompting. 

In a statement on Grok's X account later that month, the company apologized "for the horrific behavior that many experienced."

A US judge has cleared the way for a trial to consider OpenAI legal claims accusing Musk -- a co-founder of the company -- of waging a "relentless campaign" to damage the organization after it achieved success following his departure.

The litigation is another round in a bitter feud between the generative AI start-up and the world's richest person.

Musk founded xAI in 2023 to compete with OpenAI and the other major AI players.