The son of Yemeni ex-president Ali Abdullah Saleh, who was killed by the armed Houthi movement after switching sides in the civil war, called for revenge against the Iran-aligned group on Tuesday, Saudi-owned al-Ekbariya TV quoted him as saying.
It was not immediately possible to verify the authenticity of the report.
"I will lead the battle until the last Houthi is thrown out of Yemen ... the blood of my father will be hell ringing in the ears of Iran," Ahmed Ali Saleh was quoted as saying.
He called for his father's backers to "take back Yemen from the Iranian Houthi militias".
The veteran former leader was killed in a shooting attack on Monday after switching sides, abandoning his Houthi allies in favour of a Saudi-led alliance.
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Mr Saleh's death deepens the complexity of the multi-sided war, with much depending on the future allegiances of his loyalists.
The Saudi-led coalition was counting on him to give them an edge in the conflict.
Mr Saleh had a wide following in Yemen, including army officers and armed tribal leaders who once served under him, and his allies may still be able to have some impact on the war.
Ahmed Ali has lived under house arrest in the United Arab Emirates, where he once served as ambassador before it joined ally Saudi Arabia to make war on the Houthis, who until this week had ruled much of Yemen together with Mr Saleh.
Political sources say he had been held incommunicado and under guard at a villa in the UAE capital, Abu Dhabi.
His reported first public statement may indicate that his former enemies in the coalition are unleashing him against the Houthis.
The UAE is a key member of the mostly Gulf Arab alliance that sees the Houthis as a proxy of their arch-enemy Iran but had struggled to make gains against the Houthi-Saleh alliance despite thousands of air strikes backed by U.S. and Western arms and intelligence.
Ahmed Ali, the powerful former military commander of Yemen's elite Republican Guards, appeared to have been groomed to succeed his father, and he may be the family's last chance to win back influence.
The whereabouts of Saleh's other key relatives, who had led six days of street battles against the Houthis in the capital Sanaa before their rout on Monday, were unknown.
Residents reported that fighting had subsided but that Saudi-led coalition jets pounded several targets, including the downtown presidential palace where a governing body led by Houthi-Saleh politicians had regularly convened.
The Houthi leader, Abdul Malik al-Houthi, hailed Saleh's death in a speech on Monday as a victory against a treasonous conspiracy by Yemen's Saudi enemies and called for a mass rally on Tuesday at a parade ground near the site of the air strikes.
He also reached out to Mr Saleh's political party and said his movement had no quarrel with it, underscoring the influence Mr Saleh's allies still have in Yemen.
Warplanes strike Sanaa
Saudi-led warplanes pounded the rebel-held Yemeni capital before dawn on Tuesday after the rebels killed Mr Saleh, residents said.
Exiled President Abedrabbo Mansour Hadi called on Yemenis to unite against the Iran-backed insurgents.
At least seven strikes hit the presidential palace in a densely populated residential neighbourhood in the heart of Sanaa, witnesses said.
There was immediate word on any casualties.
The streets emptied before dark on Monday as coalition aircraft swooped low over the city.
There were a few minor clashes between the Houthis and Saleh supporters in southern districts which had been loyal to the strongman.
But there was no repetition of the heavy fighting that had rocked the capital for the five previous nights, residents said.
'Criminal nature'
Arab League chief Ahmed Abul Gheit on Tuesday condemned the killing of Yemen's former president Ali Abdullah Saleh by Houthi rebels, saying it illustrated their "criminal nature".
The head of the pan-Arab bloc warned Mr Saleh's killing as he fled the capital Sanaa on Monday following the collapse of his uneasy alliance with the rebels threatens an "explosion in the security situation" in the war-ravaged country.
Mr Saleh's "assassination and the way it was done reveals to everyone the criminal nature bereft of humanity of that militia which constitutes the main reason for the devastation that has ravaged the country," Mr Gheit said in a statement.
The Shiite Houthi rebels moved swiftly to consolidate their control over Sanaa after nearly a week of deadly clashes with Saleh loyalists.
Mr Saleh, who had ruled Yemen for three decades, joined forces with the Houthis in 2014 when they took control of large parts of the country, including the capital.
But that alliance unravelled over the past week, with dozens reported dead in clashes as Mr Saleh reached out to the Saudi-led coalition that has waged devastating air strikes against the Houthis since September 2015.
Yemen's war has left thousands dead since 2015, led to one of the world's worst humanitarian crises and deepened tensions between Middle East rivals Saudi Arabia and Iran.
