Mark Zuckerberg has said he is “not holding his breath” over a proposed cage fight with Elon Musk, as he revealed that he had suggested a date of 26 August for the contest.

The Facebook co-founder posted on the Threads app that he was “ready today” for a bout but that he had not received confirmation from the Tesla chief executive and world’s richest man.

“I’m ready today. I suggested August 26 when he first challenged, but he hasn’t confirmed. Not holding my breath,” he wrote on Sunday.

Musk added to the confusion by tweeting on Monday that he “may need surgery before the fight can happen” due to problems with his neck and upper back.

Musk had challenged Zuckerberg to a cage fight in June, prompting his rival to reply: “Send me location.” Details about whether and when a cage brawl will take place, or whether it was just online jousting between billionaires, have been vague ever since.

Musk prompted a renewed exchange of social media posts over the mooted fight when in the early hours of Sunday he wrote on the rebranded Twitter that the contest would be livestreamed on his platform. Last month Musk announced that Twitter had been rebranded as X.

Musk added in his post that all proceeds from the fight would go to army veterans.

The Musk post prompted replies on Threads – an app nicknamed the “Twitter killer” – from Zuckerberg, including the “not holding my breath” post. A further post took a swing at tech glitches that have hit Twitter since Musk bought the platform for $44bn last year, with Zuckerberg suggesting

:“Shouldn’t we use a more reliable platform that can actually raise money for charity?”

However, Zuckerberg’s 26 August date was looking unlikely on Monday – even if both men were serious about the fight – after Musk tweeted that he needed an MRI scan and that the exact date was “still in flux.”

Last year Musk tweeted that a sumo wrestling bout had caused him “eight years of mega back pain” that required two vertebrae to be fused. Zuckerberg is a devotee of mixed martial arts – MMA professionals fight their contests in a cage – and has posted pictures of himself training with MMA professionals.