Former president Saleh and the Yemeni military fought the Houthi rebels five times from 2005 to 2014, before becoming allies after the Saudi-led coalition took military action in March 2015 to restore President Hadi to power, who had been ousted and imprisoned by the Houthis.
Activists also published pictures and a video showing Saleh's body as gunmen put it behind a wheel amid cheers, in a scene reminiscent of the death of former Libyan leader Muammar Gaddafi in October 2011.
An urgent meeting will be held soon in Iran between Qatar's Minister of State for Defense Khalid al-Attiyah, Commander of the Iranian Revolutionary Guard Corps (IRGC) Mohammad Ali Jafari, and representatives of Hezbollah and Houthi rebels, according to informed sources.
Gun battles between the Houthis and Saleh loyalists erupted in the capital Sanaa on December 3 as residents reported a "street war" between the former allies.
The circumstances of Saleh's death were unclear but Houthi officials said their forces caught up with him as he tried to flee capital city Sanaa.
The source said Saleh's death did not mean the end of the "revolution" against the Houthis, and stated Saleh was now a "martyr of the country".
The wider Yemen conflict pits the Houthi-Saleh alliance against the Saudi-backed government of Hadi.
Saleh said Saturday that he was ready to talk to the Saudi-led coalition if it lifts a crippling blockade imposed on the impoverished country last month after a rebel missile was shot down near Riyadh.
A senior official with Yemen's internationally-recognized government confirmed to The Associated Press that Saleh had been killed.
Yemen expert Nadwa Dawsari, of non-profit Project on Middle East Democracy, said Saleh's killing could have grave consequnces for the country. But he recently switched his alliance to Saudi Arabia, which has led a three-year bombing campaign against the Houthis in Yemen and implemented a blockade of Yemeni ports.
Saleh ruled Yemen for more than three decades until he was forced to resign following the Arab Spring uprising of 2011.
In this January 3, 2017 file photo, tribesmen loyal to Houthi rebels chant slogans during a gathering aimed at mobilizing more fighters into battlefronts to fight pro-government forces.
Saudi Arabia views the Houthis as an Iranian proxy located just next door.
The former president of Yemen and a main player in its long-running civil war has been killed after an enemy faction attacked his house, according to reports.