Houthi rebels claim they have gained control of most of Yemen's capital Sanaa, a claim denied by forces loyal to the country's former President Ali Abdullah Saleh.
The video, apparently shot by one of the attackers, showed a Houthi crowd picking up Saleh's dead body, wrapped in a colorful blanket, off the ground and lifting it onto a pickup truck. The man had suffered a large head wound.
Without mentioning Saleh by name, he said that he knew about Saleh's communication with the coalition and his efforts to turn against the Houthis.
"The Interior Ministry announces the end of the crisis of militias and the killing of their leader and a number of his criminal supporters", an anchor said on the rebels' Al-Masirah television, referring to armed supporters of Saleh.
The Dubai news channel said the sources said Saleh was killed in fighting against the Iran-aligned Houthi group in the capital Sanaa, but gave no further details.
BBC World Service journalist Mai Noman said: "Saleh's death: shocking not just bec he ruled #Yemen for over 30yrs, he's been the key player in every major event even after being ousted".
The GPC source said he was killed while on his way to his birth village, Sanhan, south of Sanaa.
In a televised interview, Salah also called for resuming relations with Saudi Arabia, if the Saudi-led coalition lifts its blockade of Yemeni ports and air facilities.
Yemen ex-president Ali Abdullah Saleh killed by rebel forces
Former Yemen President Ali Abdullah Saleh's has been reported killed.
Former Yemeni president Ali Abdullah Saleh officially broke with his Houthi militia allies, calling on his supporters to rise up against them across the country.
The Huthis quickly hit back, accusing Saleh of staging a "coup against our alliance".
The Houthis had branded him a traitor for allegedly striking a deal with Saudi Arabia.
Tribal forces have meanwhile mobilized to support Saleh.
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.
In a televised address, Saleh called for new relations with the Saudi-led coalition, which he and the Houthis have been battling for nearly three years (since March 2015).