According to Houthi media, fighters blew up Saleh's house in Sanaa earlier on Monday, amid aerial attacks by Saudi-led coalition warplanes acting in support of the former president.
The Yemeni interior ministry said in a brief statement,"The end of the treason militias and the killing of its leader", referring to the General People Congress Party, which Saleh led.
Graphic video shared on social media showed the body of Saleh being carried in the back of a pick-up vehicle.
Saudi-owned al-Arabiya television has quoted sources in former President Ali Abdullah Saleh's party as confirming he had been killed.
The Associated Press also reported the death. The news that Saleh had been killed came just hours after Saudi Arabia made a decision to back Saleh, calling his fight against the Houthis a "popular uprising".
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.
"I can hear heavy shelling outside now and know it is too imprecise and too pervasive to guarantee that any of us are safe", she said.
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The officer pulled the auto over and took Rodriguez into custody without incident, the sheriff's office said. As of Friday, the teen was being held in police custody until a reunion with her family could be arranged.
The Houthis had branded him a traitor for allegedly striking a deal with Saudi Arabia.
The 75-year-old Saleh had previously ruled Yemen for more than three decades after the country's unification but was toppled in 2012 after popular and political pressure during the so-called Arab Spring. He remained in the country, however, and continued to wield power from behind the scenes.
Yemen's then President Ali Abdullah Saleh gestures during a gathering of supporters in Sanaa February 20, 2011.
Qatar's Emir Tamim bin Hamad attempted to mediate to end the tension between the two conflicting forces loyal to Ali Abdullah Saleh and Houthis in Sanaa.
Saudi Arabia views the Houthis as an Iranian proxy located just next door.
The stalemated war has killed more than 10,000 civilians and displaced 3 million.
More than 40 Houthi combatants were killed and dozens were injured in clashes that took place in Sanaa on Saturday, December 2, between the Houthis and the militias of ousted Yemeni President Saleh, according to MENA.