Unable to defeat the loyalists of former president Ali Abdullah Saleh, aided by Houthi rebels the Saudis claim are backed by Iran, the coalition has imposed a blockade on Yemen.
Fighting erupted between the Iranian-allied Shiite rebels and forces loyal to Ali Abdullah Saleh last week, unraveling their fragile alliance, formed in the face of the internationally-recognized government and Saudi-led coalition.
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.
New checkpoints manned by rebels sprung up across Sanaa on Tuesday as their leaders hailed their control of the capital, rallying supporters and pledging that backers of Saleh were safe.
It was not immediately clear if the rebels would allow Saleh's family to hold a funeral later in the day.
Saleh's body, which had appeared in a video by the militias with a gaping head wound, was taken to a rebel-controlled military hospital.
Since March 2015, Saudi Arabia and some of its Arab allies have been carrying out deadly airstrikes against the Houthi Ansarullah movement in an attempt to restore power to fugitive former president Abd Rabbuh Mansour Hadi, a close ally of Riyadh.
United Nations spokesman Stephane Dujarric told reporters Tuesday that Ismail Ould Cheikh Ahmed called the killing of Yemen's former President Ali Abdullah Saleh and others "an adverse development" that will "constitute a considerable change to the political dynamics in Yemen".More news: Jimmy Smith receives 4-game suspension
Saleh was killed on Monday after he tried to break off the alliance with the Houthis and negotiate with the Saudi coalition.
At least 13 other journalists and media workers are now held hostage in Yemen by armed groups, including the Houthis and al-Qaeda.
Saleh ruled Yemen for more than three decades until an Arab Spring uprising forced him to step down in 2012.
The 75-year-old had survived a civil war, rebellion in the north, an Al-Qaeda insurgency in the south and a June 2011 bomb attack on his palace that wounded him badly.More news: 2 militants killed, soldier, civilian injured in Qazigund
Saleh on Saturday announced he was open to talks with Saudi Arabia and its allies on condition they ended their crippling blockade of Yemen's ports and airports.
The Houthis and Saleh's forces began fighting each other in Sanaa last week. The coalition threw its support behind Saleh when he turned on the rebels, and may now back his son.
The war and blockade has plunged Yemen into a major humanitarian disaster, leaving 20 million people in need of aid.
A least 234 people were killed in fighting that the International Committee of the Red Cross described as the fiercest since the start of the conflict.More news: Time announces Person of the Year finalists
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