SWEIMEH, Jordan — A day after Houthi rebels in Yemen killed former President Ali Abdullah Saleh, his son was reported Tuesday to have emerged from enforced seclusion in the United Arab Emirates and to have vowed to avenge his father’s death.

The son, Ahmed Ali Saleh, once a powerful military commander, made the pledge as warplanes from a Saudi-led coalition bombed Sanaa, the Yemeni capital, news reports said, striking targets including the presidential palace.

The level of fighting on the streets of the city seemed to be lower than in preceding days, after Ali Abdullah Saleh switched his allegiance from the Iranian-aligned Houthi rebels holding the capital to the Saudi-led forces seeking to expel them.

The move cost him his life, as Houthis turned their fury on him for what they considered a betrayal. Although the precise sequence of events surrounding Saleh’s death remained unclear, a video broadcast by the rebels showed his body dumped in the back of a pickup truck.

His son, quoted by the state-run Al Ekhbariya television station in Saudi Arabia, said, “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,’’ he added. There was no immediate confirmation of the TV report.

Ahmed Ali Saleh had military training in the United States and once led Yemen’s Republican Guard. He later became his country’s ambassador to the United Arab Emirates.

In a separate statement delivered to Reuters, the news agency reported, the son also vowed to “confront the enemies of the homeland and humanity, who are trying to obliterate its identity and its gains and to humiliate Yemen and Yemenis.’’