Saudi-led coalition provides air-cover for Saleh's forces in Yemen
It follows Saleh's announcement on Saturday that he was ready to turn a "new page" in ties with the coalition fighting rebels in Yemen if it stopped attacks on his country.
The comments have been welcomed by Riyadh and such moves could pave the way for an end to nearly three years of war in Yemen.
The apparent shift in position came as Saleh's supporters battled his former Houthi allies in Hadda, a district in southern Sanaa where members of Saleh's family, including his nephew Tareq, live.
It was the fourth day of clashes sparked by what Saleh's General People's Congress (GPC) called an attempt to seize a main mosque in the city.
The fighting has killed dozens of people and wounded hundreds, according to the International Committee of the Red Cross, and raised concern of further casualties among civilians.
Tension between Saleh and the Houthis has been rising in recent months. Saleh has accused the Houthis of seeking to monopolise power and the rebels have accused the strongman of treason over his suspected contacts with Saudi Arabia and the UAE.
The Saudi-led coalition - which has fought Saleh and the Houthi rebels since 2015 - last month imposed a total blockade on the impoverished country after a rebel missile was shot down near Riyadh.
The clashes had added a new layer to an already complex situation in Yemen, the poorest country in the Middle East.
A proxy war between the Iran-aligned Houthis and the Saudi-backed Hadi has worsened the situation and caused one of the worst humanitarian crises in recent times.
Saleh's announcement was welcomed by the coalition, which has struggled to achieve any progress against the Houthi-Saleh alliance that had controlled most of northern Yemen since 2015 and forced President Abd Rabbo Mansour Hadi to flee into exile.
The Saudi-owned Al-Arabiya television said coalition aircraft pounded Houthi outposts in southern Sanaa, but gave no details on casualties. Residents reported at least five air strikes shook the highlands of the area.
Yemen's war has killed more than 10,000 people since 2015, displaced more than two million people, caused a cholera outbreak infecting nearly one million people and led the country to the brink of famine.