BEIRUT (Reuters) - Hundreds of angry protesters burnt tyres and blocked roads across Lebanon Tuesday after a Hezbollah-backed politician was named prime minister, shifting the balance of power in the country towards Syria and Iran. The nomination of Najib Mikati is seen as a victory for Hezbollah, which is trying to fend off a UN-backed tribunal set up in 2005 to try the killers of statesman Rafik al-Hariri and which is expected to accuse members of the Shia group. Sunni Muslims loyal to outgoing premier Saad al-Hariri, Rafiks son who has Western and Saudi backing, staged a day of rage to protest the appointment of Sunni billionaire Mikati, a centrist lawmaker with ties to both Saudi Arabia and Syria. Hezbollahs enhanced political strength will set off alarm bells in Washington and across the region, especially in Israel which in 2006 fought a five-week war in a failed attempt to destroy the Iran-backed movements formidable military capacity. Israeli officials have since threatened regularly to respond to Hezbollahs arsenal of rockets in Lebanon, upgraded with help from Syria and Iran. Mikati, a telecoms tycoon who has portrayed himself as a consensus candidate, said he would start talks to form a government Thursday and appealed to all Lebanese factions to overcome their differences. All Lebanese leaders should cooperate together to face the current challenges, he said from the presidential palace after he accepted his nomination by President Michel Suleiman. I reiterate my position ... that my hand is extended to all factions to take part and end division...through dialogue. Hezbollah leader Sayyed Hassan Nasrallah urged Mikati to form a national partnership government. Nasrallah said Mikati was not the Shia groups candidate, but it had backed him as a compromise figure. Hezbollah and its allies did not want to break bones with the other side ... (nor) form a one-sided government, he said. France said it was important that the new government was formed free from interference and through dialogue. We urge the incoming government to respect international commitments made by Lebanon, and particularly for the Special Tribunal for Lebanon, French foreign Ministry spokesman Bernard Valero said. Hezbollahs role in bringing down Hariris government will also raise concerns in Sunni Arab states, wary of Irans influence in the region. The biggest protest took place in the northern city of Tripoli where medical sources said 20 people were treated for injuries and protesters set fire to a satellite truck used by the Arab television channel Al Jazeera. Hariri appealed for calm, saying he rejected demonstrations of violence. You are angry but you are responsible people. I understand your feelings, he told supporters in a televised speech.This anger should not lead us to what disagrees with our values ... our belief that democracy is our refuge. Sunni blood is boiling chanted protesters in Tripoli, urging Mikati to withdraw his nomination and waving flags of Hariris Future Movement which says it will not serve in any government dominated by the militant Shia group. In Beirut, protesters blocked a road with burning tyres and overturned garbage containers. A security source said shots were fired in the air and the army intervened, but no one was hurt. Lebanons power-sharing political system calls for the post of prime minister to be held by a Sunni, and Hariri supporters said any figure who accepted the nomination from the Shia group to form a new government would be considered a traitor.Hariri supporter Mustafa Alloush told the crowd in Tripoli Tuesday that the overthrow of the govt two weeks ago was part of an Iranian takeover. Its an attempt to bring Lebanon into the Persian sphere, he said.