Houthi TV announced the "killing of the treacherous leader Ali Abdullah Saleh and his supporters".
The Houthis accused Saleh of a coup on Saturday after he said he was open to talks with the Saudi-led military coalition backing Mr Hadi's government.
His home in Sana'a was blown up during an attack, according to a Houthi-run television station.
Iranian, Russian and Arab media said Saleh may have been at the permanent headquarter of the General People's Congress in Sana'a where he has been killed.
This is the first such airdrop in Sanaa since the start of the fighting three days ago and the ferocious fighting in the country's capital might enter a new phase following the Saudi intervention with providing logistical support for Saleh, according to local observers.More news: Jose Mourinho Pondering Luke Shaw Start Against CSKA Moscow
The former president's militiamen, however, failed to do so and Ansarullah revolutionaries managed to restore security to the capital, accusing Saleh, whose whereabouts are unknown, of betraying an alliance aimed at confronting a brutal Saudi-led aggression on the Arab impoverished country.
The Saudi-led air campaign, backed by USA and other Western arms and intelligence, has killed hundreds of civilians but has failed to secure the coalition any major gains in the almost three-year-old campaign to restore Yemen's internationally recognised president, Abd-Rabbu Mansour Hadi, to power.
Internal rifts have shaken the fragile alliance between the Houthis and Saleh loyalists, who joined ranks in 2014 to seize Sanaa.
Residents in the capital of Sanaa mired in the humanitarian catastrophe said that they had witnessed the explosion at Saleh's home.
Aid flights in and out of Sanaa airport had been suspended, the world body said in a statement following its appeal for a humanitarian pause on Tuesday.More news: American Airlines Resolves Problem That Could Have Canceled Thousands of Flights
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.
At the United Nations, U.N. Secretary-General Antonio Guterres urged the warring parties to stop all ground and air assaults.
A military commander loyal to Saleh told Xinhua by phone saying that "overnight, the coalition planes airdropped weapons and different kinds of communications equipment to the commanders who are leading the anti-Houthi uprising in Sanaa".
Circumstances for the alleged death of Saleh, who was the leader of Yemen and its precursor Yemen Arab Republic for decades and cooperated with the USA, were not immediately clear.
Saleh and the Shi'ite Muslim Houthis had made common cause against Hadi loyalists.More news: Nebraska reportedly hiring UCF's Scott Frost as new head coach
Iran supports the Houthis politically but denies that it has helped to arm the rebel group. Houthi tanks have been firing and the shells were falling on our neighbourhood, ' said Mohammed al-Madhaji, who lives in the Political District.
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