The son of Yemen's former president Ali Abdullah Saleh, who was killed earlier this week, vowed in a written statement to "confront enemies of the homeland".
Ahmed Ali, a former commander of Yemen's elite Republican Guards, said that his father had died at his house, while carrying his weapon.
Referring to the Iran-aligend Houthi group which killed his father, Ahmed Ali said he would "confront the enemies of the homeland and humanity, who are trying to obliterate its identity and its gains and to humiliate Yemen and Yemenis".
He also vowed to lead a campaign against the movement which carried out the killing after he switched sides in the civil war.
The intervention by Mr Saleh, a former leader of the elite Republican Guard once seen as a likely successor to his father, gives the anti-Houthi movement in Sanaa a potential figurehead, after a week of fighting that saw the Houthis rout Saleh's supporters in the capital.
Yemen's war, pitting the Iran-allied Houthis who control Sanaa against a Saudi-led military alliance backing a government based in the south, has brought what the United Nations calls the world's worst humanitarian crisis.
The world body says millions of people may die in one of the worst famines of modern times, caused by warring parties blocking food supplies.
Saleh had helped the Houthis win control of much of the country's north including Sanaa, and his decision to switch allegiances and abandon the Houthis in the past week was the most dramatic change on the battlefield in years. But the Houthis swiftly crushed a pro-Saleh uprising in the capital and shot him dead in an attack on his convoy.
Tens of thousands of Houthi supporters staged a rally in the capital to show support for their leader and celebrate the death of Saleh. They chanted slogans against Saudi Arabia and its allies.
Mahmoud Ali al-Houthi, head of the movement's Revolutionary Committee, denied allegations that the group was executing members of Saleh's party after their capture: "We have been treating some of Saleh's sons and we haven't executed them," he told the crowd.
Sanaa saw no fresh fighting after five days of combat that the Red Cross said killed more than 230 people. The Saudi-led coalition struck the city with 25 air strikes overnight, but United Nations (UN) and Red Cross aid flights were able to land at the airport, UN humanitarian coordinator in Yemen Jamie McGoldrick said.
"People are now emerging from their houses after five days being locked down basically as prisoners," Mr McGoldrick said. "They are now seeking safety, moving their families in case things erupt again and at the same time seeking medical treatment and trying to pacify very terrified kids who have endured five days of relentless shelling, shooting and ground fire and air strikes."
The Saudi cabinet, in a statement that did not mention Saleh by name, said it hoped the Sanaa uprising against the Houthis would "help rid sisterly Yemen of repression, death threats, ... explosions and seizure of private and public property".
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