The GPC officials said Saleh was killed south of the capital Sanaa along with the assistant secretary-general of the GPC, Yasser Al-Awadi.
Sources in the Houthi group said fighters stopped his armored vehicle with an RPG rocket and then shot him dead.
A Houthi video distributed on social media showed what appeared to be Saleh’s body, clad in grey clothes and being carried out on a red blanket. The side of his head bore a deep wound.
Unverified footage that circulated earlier on social media showed armed militiamen unfurling a blanket containing the corpse and shouting, “Praise God!” and “Hey Ali Affash!,” another last name for Saleh.
In a televised address Monday evening, Yemeni President Abed Rabbo Mansour Hadi called on all citizens in all provinces of the country to rise up against the Houthi militias.
The radio station of the Houthi-run Yemeni Interior Ministry first reported Saleh’s death but his party quickly denied this to Reuters, saying he was still leading his forces in Sanaa.
Earlier on Monday, Houthi forces blew up Saleh’s house in Sanaa and came under aerial attack by Saudi-led coalition warplanes for a second day, residents said.
Saleh’s loyalists have lost ground on the sixth day of heavy urban warfare with the Houthis during which the death toll has jumped to at least 125 with 238 wounded, according to the International Committee of the Red Cross.
“We are supporting the main hospitals in Sanaa who urgently need war-wounded kits,” ICRC spokeswoman Iolanda Jaquemet said in Geneva. “We are also looking at donating dead body bags to hospitals which are actually asking for them and hope to donate fuel to the main hospitals because they depend on generators.”
The United Nations called for a humanitarian pause in Sanaa between the hours of 10 a.m. and 4 p.m. to allow civilians to leave their homes, aid workers to reach them, and the wounded to get medical care.
STREETS ARE “BATTLEGROUNDS“
Jamie McGoldrick, UN humanitarian coordinator in Yemen, said in a statement that the streets of Sanaa had become “battlegrounds” and that aid workers “remain in lockdown.”
McGoldrick warned the warring parties that any deliberate attacks on civilians and against civilian and medical infrastructure are “clear violations of international humanitarian law and may constitute war crimes.”
Sanaa residents reported intense fighting overnight and into the morning with families cowering in their homes as explosions rocked the city. Coalition air strikes hammered Houthi positions in an apparent bid to shore up Saleh’s forces, witnesses said.
The realignment of Saleh’s forces with the Saudis would mark a significant turn in a war that is part of a wider struggle between regional powers Saudi Arabia and Iran.
Yemen’s protracted bloodshed has compounded the woes of one of the Arab world’s poorest countries and left at least 10,000 dead as hunger and disease have spread.
At the United Nations, UN Secretary-General Antonio Guterres urged the warring parties to stop all ground and air assaults. He also called for the resumption of all commercial imports into Yemen, saying millions of children, women and men were at risk of mass hunger, disease and death.
However, in a speech late on Sunday, Saleh formally annulled his alliance with the Houthis and pledged to step up his fight.
Saleh, who dominated Yemen’s heavily armed tribal society for 33 years before quitting in the aftermath of the Arab Spring uprisings in 2011, and the Shiite Muslim Houthis had made common cause against Hadi loyalists.
But they vied for supremacy over the territory they ran together, including Sanaa, which the Houthis seized in September 2014, and their feud burst into open combat on Wednesday.
Houthi spokesman Mohammed Abdul Salam claimed significant gains in the battle for Sanaa on Monday.
“With the aid and approval of God, the security forces backed up by wide popular support were able last night to cleanse the areas in which the militias of treason and betrayal were deployed,” he said in a statement.
The Houthi movement’s TV channel Al-Masirah and witnesses said Houthi fighters had seized the downtown home of Saleh’s nephew Tareq, an army general.
Residents said the warring sides traded heavy automatic and artillery fire as the Houthis advanced in the central Political District, which is a redoubt of Saleh and his family.
“We lived through days of terror. Houthi tanks have been firing and the shells were falling on our neighborhood,” said Mohammed Al-MadHajji, who lives in the frontline district.
“The fighting has been so violent we feel we could die at any moment. We can’t get out of our homes.”
Houthi media and political sources also reported that the Houthis also advanced toward Saleh’s birthplace in a village outside Sanaa where he maintains a fortified palace.