Fighting has intensified since former Yemeni President Ali Abdullah Saleh, an erstwhile Houthi ally who had turned on the group, was killed in an attack on his convoy last week.
There are expectations in Yemen that Maj Gen Saleh will now return to Yemen to lead a battle against the Houthis to take revenge for the killing of his father.
Air raids also struck northern provinces including Taiz, Haja, Midi and Saada, the rebel-owned channel said, although there was no immediate word on casualties.
Both Saleh and Houthis benefited from their four-year alliance as Saleh got Houthis manpower and firepower while Houthis gained from Saleh's governing and intelligence networks.
Photos and Videos of the brutal assassination went viral on social media, shortly after announcing his death by the rebel militia.
The gruesome images from the previous day sent shockwaves among Saleh's followers - a grisly end recalling that of his contemporary, Libya's Moammar Gadhafi, in 2011.
Saleh, who ruled Yemen for more than three decades, allied with Houthis after an Arab Spring uprising forced him to resign in 2012.
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The killing of Yemen's ex-President Ali Abdullah Saleh by the country's Shiite rebels as their alliance crumbled has thrown the almost three-year civil war into unpredictable new chaos.
Saleh's vehicle was struck by an RPG fire on Monday and he was later shot to death, raising questions about what happens next in the almost three-year war that has killed at least 10 000 people.
In other areas like Fag Attan, Saleh's forces are still surrounded by Houthis. The coalition threw its support behind Saleh when he turned on the rebels, and may now back his son. The Houthis' top leader, Abdul-Malek al-Houthi, said Saleh paid the price for his "treason", accusing him of betraying their alliance to side with the Saudi-led coalition.
It also shatters hopes by Yemen's Saudi-backed government that Saleh's recent split with the Iranian-backed rebels, known as Houthis, would have weakened them and given the government and the Saudi coalition backing a chance for a turning point in the stalemated war that has brought humanitarian disaster.
From the Saudi capital, Riyadh, where he has been in self-imposed exile for most of the war, Hadi tried on Monday to rally Saleh's allies to keep up the fight against the Houthis.
Jamie McGoldrick, of United Nations aid agency OCHA, said civilians in Sanaa are "emerging from their houses after five days being locked down, basically prisoners", to seek safety, medical care, fresh water and other survival needs.
The International Committee of the Red Cross says that as many as 234 people have been killed in Yemen's capital, Sanaa, in street fighting this month between the country's Shiite rebels and the supporters of the slain former president, Ali Abdullah Saleh.