"The general public in Yemen is seeking a transfer of power to the vice president," Gen. Ali Mohsen al-Ahmer told CNN. "This is a principle that we must follow because there are agreements that sides have signed."
Ahmer insisted on full implementation of the Gulf Cooperation Council's plan to oust Saleh and hold elections.
Under the GCC plan, Saleh is to hand over power to a transitional government after 30 days. But in May, after some members of his party signed the deal, he refused.
Vice President Abdu Rabu Mansoor Hadi, whom the general praised as "our brother," has been acting leader since Saleh was wounded in a June 3 assassination attempt and went to Saudi Arabia for treatment.
Ahmer said "all sides agree on him and all respect him" to head the interim leadership.
Saleh says he will return.