The six-nation Gulf Cooperation Council (GCC) has proposed the formation of a government of national unity in Yemen, Saleh transferring his powers to his vice president, and an end to deadly protests rocking the impoverished country.
Under the GCC initiative, the president would submit his resignation to parliament within 30 days, with a presidential vote to be held within two months.
"The GPC and its allies have accepted the GCC initiative in its entirety," Soltan al-Barakani, the party's deputy secretary general and head of its parliamentary bloc.
Yemen's Foreign Minister Abu Bakr al-Kurbi was in Abu Dhabi, where he was expected to tell his United Arab Emirates counterpart of the decision, Barakani added. The UAE currently holds the rotating presidency of the GCC.
The White House on Saturday welcomed the plan for Yemen's longtime president to step down, urging all sides to "swiftly" implement a peaceful transfer of power.
"We applaud the announcements by the Yemeni Government and the opposition that they have accepted the GCC-brokered agreement to resolve the political crisis in a peaceful and orderly manner," White House spokesman Jay Carney said in a statement.
"The United States supports a peaceful transfer of power in Yemen that is responsive to the aspirations of the Yemeni people."
Carney also urged "all parties to move swiftly to implement the terms of the agreement so that the Yemeni people can soon realize the security, unity, and prosperity that they have so courageously sought and so richly deserve."
US State Department spokesman Mark Toner earlier said "the timing and form of this transition should be identified through dialogue and begin immediately."
He also called for "genuine participation" from all sides and urged them to refrain from violence.
On Friday, Saleh gave a cool response to the Gulf plan for him to quit, even as massive crowds returned to the streets to demand his immediate ouster.
A spokesman for the opposition Common Forum coalition said on Friday that "forming a national unity government while the president is still in office is not accepted."
"The president's departure is essential to any solution," he told AFP.
A defiant Saleh, who has ruled Yemen for 32 years, has publicly insisted on sticking to the constitution in any transfer of power.
US officials are alarmed at the fallout from the upheaval in Yemen, where Al-Qaeda has already exploited the violent power struggle between Saleh and his opponents.
Army gunfire wounded two protesters on Saturday in the southern Yemeni port city of Aden during a general strike called by the opposition.
A medic said soldiers opened fire on a group of youths who had been trying to erect a barrier to halt traffic, wounding two of them.
Barricades already blocked vehicles along the main thoroughfares of Aden, a centre of almost three months of protests against Saleh's iron-fisted regime.
The city was virtually paralysed, with shops, schools and government offices closed.
The strike was also well-observed in the northern provinces of Lahij and Abyan, while student protesters took to the streets of Taez, a restive city in the southwest, residents said.
However, there were few signs on Saturday of any interruption in the capital Sanaa, an AFP correspondent said.