OAKLAND, California (Reuters) - OpenAI and Elon Musk have agreed to fast-track a trial over OpenAI's for-profit shift, the latest turn in a grudge match between the world's richest person and OpenAI CEO Sam Altman playing out publicly in court.

Billionaire Elon Musk and OpenAI jointly proposed a trial in December, according to a federal court filing on Friday.

The parties agreed to delay a decision on whether the expedited case will be decided by a jury or solely by the judge, said the filing in U.S. District Court for the Northern District of California.

The judge this month denied Musk's request to pause the artificial intelligence group's transition to a for-profit model but agreed to an expedited trial in the autumn, the latest turn in the high-stakes legal fight.

"We welcome the court's March 4 decision rejecting Elon Musk's latest attempt to slow down OpenAI for his personal benefit," OpenAI said in a blog post on Friday.

Musk cofounded OpenAI with Altman in 2015 but left before the company took off and subsequently founded the competing startup xAI in 2023. 

Last year, the CEO of Tesla and owner of the X social media platform sued OpenAI and Altman, accusing OpenAI of straying from its founding mission - to develop AI for the good of humanity, not corporate profit.

OpenAI and Altman have denied the allegations, while Altman alleges that Musk has been trying to slow down a competitor.

At stake in the lawsuit is the ChatGPT maker's transition to a for-profit model, which the startup says is crucial to raising more capital and competing well in the expensive AI race.

OpenAI's last fundraising round, of $6.6 billion, and a new round of up to $40 billion under discussion with SoftBank Group, are conditioned on OpenAI restructuring to remove the nonprofit's control.  

Friday's filing comes weeks after Altman, who has said OpenAI is not for sale, rejected a $97.4 billion unsolicited takeover bid from a Musk-led consortium with a "no thank you."

(Reporting from Anna Tong in Oakland and Devika Nair in Bengaluru; Editing by William Mallard)