The development was confirmed by Saleh's General People's Congress party. He is the former general manager of Al Arabiya news channel, and former editor in chief of Asharq Al-Awsat, where this article is also published.
In a statement read out on a Houthi television network, the interior ministry announced the "killing" of "Saleh and his supporters". It gave no further details.
Yemen's Houthi rebels said they killed their ally and former Yemeni president Ali Abdullah Saleh, after their partnership that has fought a Saudi-led coalition for almost three years collapsed.
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.
"Only small pockets remain", Hussain Albukhaiti, who has close ties to the Iranian-backed Houthis, added.
Sayyid said Saleh and other top party officials had came under Houthi gunfire as they fled Sanaa.
The fresh violence has increased fears for civilian victims of Yemen's war, which has claimed more than 8,750 lives since the Saudi-led coalition intervened.
The Houthis, who are believed to be backed by Iran, stormed Sanaa in September 2014.
"The president has ordered Vice President Ali Mohsen al-Ahmar, who is in Marib (east of Sanaa), to activate military units and advance towards the capital", a presidency official told AFP, speaking on condition of anonymity.
Unverified footage circulated showing his bloodied body, just days after he tore up his alliance with the Houthis following almost three years in which they had jointly battled the Saudi-led coalition.
The end of their alliance had seemed poised to transform the fortunes of war after two years of attrition along mostly static front lines, which gave the Saudi-led coalition a new advantage over the Houthis.
Sources in the Houthi militia said its fighters stopped Saleh's armoured vehicle with an RPG rocket outside the embattled capital Sanaa on Monday and then shot him dead.
"You can not say this is the end of his political movement, but it's a very big blow", he said. He did not mention Saleh's death.
The tactical alliance between Saleh and the Houthis had often appeared fragile, with both groups suspicious of each other's ultimate motives and sharing little ideological ground.