Yemen's opposition met the promise with deep scepticism, accusing Saleh of stalling.
The impoverished Gulf nation is reeling from three months of street protests demanding Saleh's ouster.
A coalition of Gulf countries tried to mediate a deal for Saleh to stand down in exchange for immunity from prosecution. But Saleh refused to sign it, prompting the chief mediator to leave Yemen on Thursday, May 19.
Saleh spokesman Ahmed al-Sufi on Friday, May 20, said Saleh would sign the agreement during a celebration on Sunday, May 22.
Opposition spokesman Mohammed al-Sabri dismissed the pledge, accusing Saleh of "playing games with time."