"It killed everyone", said local resident Aly Al Mazhary.
The Huthis quickly hit back, accusing Saleh of staging a "coup against our alliance".
The Houthis have also seized the homes of Saleh and some of his family members in a southern district of Sanaa - the so-called Political District - which witnessed some of the heaviest clashes.
The death of a leader who played a significant role in Yemeni politics is stunning, but experts say Saleh's death won't change the face of the conflict significantly.
"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 Houthis executed Saleh and maimed his body and this is against humanity, but the Houthis do not understand humanity", said the source. He added that he had sent several warnings to Saleh.
"I call on our brothers in neighbouring countries... to stop their aggression and lift the blockade... and we will turn the page", he said in a televised speech.
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He stressed that the Houthis, also known as Ansar Allah, have no enmity toward Saleh's party, the General People's Congress, which was Yemen's ruling party under Saleh but is now divided.
The former Yemeni president's break with the Houthis came after five days of bitter clashes around the capital, Sana'a, between his supporters and those of the Iranian-backed Houthi militia.
Al Arabiya quoted a source in Saleh's GPC party as saying he was killed by a sniper. "He was trying to flee to Saudi", he said.
Unverified footage circulated on social media appeared to a show corpse resembling Saleh, wrapped in a floral-print blanket with a severe head injury. Blood stained his shirt under a dark suit. He had jointly ruled the Yemeni capital with the Iran-aligned rebels for three years. It gave no further details.
Two of Mr Saleh's associates and a third official from the government of Yemen's internationally recognised president, Abed Rabbo Mansour Hadi, have confirmed the death.
One shows a group of fighters carrying the body in a sheet proclaiming "God is Great".
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