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.
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.
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.
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.
He also reached out to Saleh's political party and said his movement had no quarrel with it, underscoring the influence Saleh's allies still have in Yemen.