May 29 (Reuters) - OpenAI said it should be allowed to keep its countersuit against billionaire Elon Musk, saying the Tesla CEO's motion to dismiss the ChatGPT maker's claims has "no grounding in facts".

In a court filing late on Wednesday, OpenAI said its countersuit - which accuses Musk of engaging in fraudulent business practices under California law - should be included in the expedited trial, rather than put on hold.

OpenAI has argued that a $97.4 billion takeover bid for the company earlier this year from a Musk-led consortium was a "sham bid" aimed at drumming up media frenzy. OpenAI alleged the bid was leaked to the media before the proposal reached OpenAI's board.

Last year, Musk, who co-founded OpenAI in 2015 but left before the firm became an AI juggernaut, sued OpenAI and its CEO Sam Altman over the company's transition to a for-profit model. He accused OpenAI of straying from its founding mission - to develop AI for the good of humanity, not corporate profit.

OpenAI in April countersued Musk, citing a pattern of harassment by Musk and asking a federal judge to stop Musk from any "further unlawful and unfair action" against OpenAI. Musk had asked a federal judge to dismiss or delay OpenAI's counterclaims until a later stage in the case.

While OpenAI earlier this month dialed back its plan to remove control by its non-profit arm, Musk's lawyer said the billionaire CEO would still proceed with his lawsuit.

(Reporting by Deborah Sophia in Bengaluru; Editing by Shounak Dasgupta)

((DeborahMary.Sophia@thomsonreuters.com))