BFnews: Presidential aide Tariq Shami told Al-Jazeera news channel that the president had agreed in principle to a proposal from the Persian Gulf Cooperation Council (PGCC), which calls for the formation of a national unity government, to be led by the opposition, and for Saleh to transfer his powers to his deputy within 30 days thereafter.
Reports say a presidential vote is to be held within two months.
He said: The president has agreed and accepted the initiative of the PGCC. He added that the opposition must first agree to the deal.
He told the Qatar-based broadcaster: The transition of power in Yemen will take some time. It needs an agreement between the national powers and the opposition at the same time. This thing will happen within 60 days if we have an agreement.
Last week, Yemen's largest opposition coalition, the Joint Meeting Parties (JMP), rejected the initiative and said they seek a clear timeline for Saleh's resignation.
In power since 1978, Saleh had himself initially rejected the initiative. But soon afterward he accepted the dialogue, which the GCC said was intended to preserve Yemen's unity, safety and stability.
Saleh's reversal made the JMP quickly announce they had reservations - namely, that the transfer of powers did not necessarily mean the president was resigning.
Earlier Saturday, Saleh accused the JMP of "wanting to cause bloodshed and push the country into a civil war which is neither in the interest of the Yemen nor the region," as protesters vowed civil disobedience to protest against his rule.
Saleh said in the speech aired on state TV: No for coups and no for stopping the development process, and yes for security, stability and peace.
He said, reiterating his pledges not to leave power until his term ends in 2013: Yes, I will leave the presidency via elections - not coups.
Saleh said: Whoever wants to rule shall then call for early presidential or parliamentary elections as ensured in the constitution.
Tens of thousands continue to protest in main public squares across Yemen, as they have been over two months, demanding the ouster of Saleh after 32 years in power.
In the south-eastern port city of Aden, people responded to calls for civil disobedience, with many shops closed and public transportation brought to a standstill.
Activists have called for civil disobedience every Saturday and Wednesday.
Residents of Abyan and Lahj provinces joined the call for civil disobedience for the first time since the beginning of anti- government rallies.
Protesters throughout Yemen have been taking to the streets for more than two months, demanding the ouster of Saleh after 32 years in power.
Many believe Saleh is rapidly losing control in Yemen as the unrest continues. The escalating crackdown on protesters by the government have left more than 100 people dead.