Since March 2015, Saudi Arabia and some of its Arab allies have been carrying out deadly airstrikes against the Houthi Ansarullah movement in an attempt to restore power to fugitive former president Abd Rabbuh Mansour Hadi, a close ally of Riyadh.
Earlier this month, US Ambassador to the United Nations Nikki Haley accused Iran of supplying Houthi rebels with a missile that was sacked into Saudi Arabia in July and called for the United Nations to hold Tehran accountable for violating two UN Security Council resolutions.
The head of the Houthis' Ansarullah group warned that the biggest victor from what he described as Saleh's "sedition" was the Saudi-led coalition.
"The decision by (Saleh's) General People's Congress to take the lead and their choice to side with their people will free Yemen of. militias loyal to Iran", the statement carried by the official Saudi Press Agency said.
The Saudi-led coalition welcomed Saleh's change of stance.
The fighting subsided by the afternoon as Saleh supporters secured control.
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The Saudi-led coalition, which has fought Saleh and the Iran-backed Houthi rebels since 2015, this month imposed a total blockade on the impoverished country after a rebel missile was shot down near Riyadh.
"It is not odd or surprising that Saleh turns back on a partnership he never believed in", the group's political bureau said in a statement.
Residents of Sanaa described heavy fighting on the streets of Hadda, a southern residential district of the Yemeni capital where many of Saleh's relatives live, early on Saturday, with sounds of explosions and gunfire heard while the streets were deserted.
He told Yemenis all across the country that if they support him, "to defend the nation, the republic and the revolution".
The Saudi-led coalition responded to Saleh's statement saying that it recognised the efforts of his General People's Congress (GPC) political party to rid Yemen of the evils of "sectarian terrorist militias", Saudi state media reported.
But the head of the Houthis' Ansarullah group warned that the biggest victor from what he described as Saleh's "sedition" was the Saudi-led coalition.
Yemen's civil war has killed more than 10,000 people since 2015, displaced more than two million people, caused a cholera outbreak infecting almost one million people and put the country on the brink of starvation.