Yemen's opposition met the promise with deep skepticism, 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 Wednesday.
On Thursday, Saleh spokesman Ahmed al-Sufi said Saleh would sign the agreement during a celebration on Sunday.
Opposition spokesman Mohammed al-Sabri dismissed the pledge, accusing Saleh of "playing games with time."