In a letter, they question the board’s competence, and accuse it of undermining the firm’s work.
They also demand Mr Altman’s reinstatement.
The sacking on Friday of a man who is one of the leading figures in artificial intelligence (AI) shocked the tech world.
The letter’s many signatories, who include senior staff, say they may themselves resign if their demands are not met.
They also state that Microsoft has assured them that there are jobs for all OpenAI staff if they want to join the company.
The board is the only aspect of OpenAI without a profit motive. The employees have shares in the company they want to sell for yachtloads of cash and while collective action to get super rich is an employee’s right, the board aren’t really the bad guys in the arrangement.