SANAA (Reuters) - 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.