Yemeni President Abd Rabbu Mansour Hadi called on Saturday for a U.N.-brokered political settlement with Shi'ite rebels as some of the worst violence seen in the capital for years raged for a third day.
The fighting, which intensified on Thursday after weeks of protests and clashes, appeared to be the biggest challenge yet to a U.N.-backed transition to democracy launched after veteran ruler Ali Abdullah Saleh stepped down in 2012.
"The right choice is through the process taking place with (U.N. special envoy) Jamal Benomar," Hadi was quoted as saying by the official Saba news agency. He described the Houthi advance into Sanaa as "inexcusable".
Insecurity and political turmoil have grown in Yemen since Arab Spring protests ousted Saleh. The Houthi insurrection is one of several security challenges in Yemen, which borders oil exporter Saudi Arabia and is struggling with a secessionist movement in the south and the spread of an al Qaeda insurgency.
The Houthis, who belong to the Zaydi sect of Shi'ite Islam, have been involved in a decade-long conflict with the Sunni-dominated government, fighting for more control and territory in the north.
Prominent figures from the mainly Sunni Muslim clan, one of the most powerful tribes in Yemen, hold senior positions in the armed forces and the government.
Shi'ite Houthi rebels clashed with the army on the outskirts of Sanaa on Thursday. The fighting escalated mainly between the Houthis and tribesmen allied with the al-Ahmar clan.
Yemen's state-run television building, which is near other vital state institutions, caught fire on Saturday after three days of mortar attacks by the Houthis.
The head of Yemen TV, Hussain Basleem, told Reuters the shelling had injured several people in the building which was surrounded by Houthi rebels. Food and water supplies were running low.
Yemeni television broadcast a written message calling on national and international organisations to intervene to save its employees from the shelling. It later also broadcast another written message asking the defence minister to intervene to free the staff members trapped inside.
In a neighbouring area close to the interior ministry where Houthis have been staging a sit-in, three mortars were fired, according to a Reuters witness. It was not immediately clear who was responsible for the shelling.
Residents and relatives of victims reported at least 16 people dead between Friday night and Saturday morning, ten of them from the same family who were trying to flee their home in Shamlan district in the north of the capital. Their mini-bus was hit by mortar fire.
Medical sources also told Reuters 13 Houthis had died on Saturday in confrontations with the army in the capital.
Officials were not immediately available to confirm the death toll.
The Ministry of Education announced it would temporarily close schools from Sunday for the safety of students and teachers, Saba reported.
The University of Sanaa, the country's biggest, was closed on Saturday after a mortar fell inside its grounds during clashes on Friday.
Late on Friday the U.N.'s Benomar, who held meetings with Houthi leader Abdulmalek al-Houthi in Saada province on Wednesday and Thursday, released a statement in which he "expressed deep regrets regarding this development, including the use of violence, while utmost efforts were underway in order to reach a peaceful solution to the crisis".
A source close to the mediation efforts said President Hadi would meet with politicians on Saturday to discuss suggestions from the Houthis on ending the conflict.
One Houthi rebel leader, Abdelmalik al-Ajri, told Reuters his group's representatives could reach the capital from Saada later on Saturday or Sunday to sign a deal to end the crisis.
In recent weeks, Houthi protesters have blocked the main road to Sanaa's airport and held sit-ins at ministries calling for the ousting of the government and the restoration of subsidies cut by the state in July as part of economic reforms.