The UN urged the coalition in a statement Saturday to "fully lift" the blockade on Yemen's red sea ports saying that partial lifting only "slows the collapse toward a massive humanitarian tragedy costing millions of lives".
Yemeni President Abdrabbuh Mansur Hadi said all those who have identified a clear position in support of the popular uprising aimed at ending the coup and the restoration of the state "will all be partners in the present and future of Yemen".
Houthis and Saleh loyalists jointly overran Sanaa and much of the country in 2014, forcing the internationally recognized government of President Abd Rabbuh Mansour Hadi to flee to Saudi Arabia.
"It's been like a street war", they said, adding that ambulances have been ferrying the wounded to hospitals.
Saleh was forced to surrender his office in 2012 amid a wave of mass protests in the country, abandoning the presidency to his Vice-President Hadi.
Officials working at the TV station say Houthis raided its headquarters.
"It is happening in coordination with it", referring to the Saudi-led coalition".
Mr Saleh said he would be ready to "turn the page" if the coalition lifted a blockade and halted its attacks.
"The meeting calls for turning a new page with all the political sides. and to form a broad national coalition that will lay the foundations for a new era and unify everyone against the coup militia", the statement said. Saleh has accused the Houthis of seeking to monopolise power and the rebels have accused the strongman of treason over his suspected contacts with Saudi Arabia.
The coalition accuses Saleh, who heads the General People's Congress party, of betraying his Arab neighbors by joining forces with the Houthi rebels. "The priority has been and still is to confront the forces of aggression".
"I appeal to the leader Saleh to show more wisdom and maturity. and not to heed incitement calls", Abdel-Malek al-Houthi said in a speech on the group's Al-Masirah TV, adding that his group was ready to sit down for arbitration and abide by any ruling.
He told Yemenis all across the country that if they support him, "to defend the nation, the republic and the revolution".
He also accused the Houthis of "terrorizing" civilians.
The conflict and a blockade by the coalition has also left more than 20 million people in need of humanitarian aid, created the world's largest food security emergency, and led to a cholera outbreak that is thought to have killed 2,211 people since April.