A day after Saad Hariri was designated to form Lebanon's next government and become its next prime minister, Prime Minister Binyamin Netanyahu - in a clear message to Beirut - told the cabinet on Sunday that if Hizbullah is included in the new coalition, Lebanon will be held responsible for the Shi'ite group's actions. "If Hizbullah joins the Lebanese government, then the Lebanese government is accepting responsibility for Hizbullah's actions, including its actions against Israel," Netanyahu told the ministers, according to a government source. The prime minister's comments came during a cabinet discussion on Hizbullah's attempts to entrench itself inside the new Lebanese government. It also came in light of rare talks on Thursday between Hariri, the son of assassinated former prime minister Rafik Hariri, and Hizbullah's head Hassan Nasrallah, to investigate the possibility of a national unity government. Netanyahu's comments, according to government officials, were meant to inform the Lebanese that if a national unity government was created, Beirut would bear responsibility for Hizbullah's actions. The official said Israel would deem Hizbullah's participation in the new government as "a matter of extreme significance." Meanwhile, supporters of Lebanon's prime minister-designate clashed with rival gunmen in the streets of Beirut on Sunday, security officials said, in a first outbreak of violence since the June 7 election. Hours earlier, Hariri, a Western-backed billionaire, was holding talks with his predecessors as part of the delicate process of forming a government that can unify the deeply divided country. Security officials had no information on casualties, but Al-Arabiya TV reported that one woman was killed and at least three people were wounded, including a Lebanese soldier. The army sent troops to the area to try to restore calm, the officials said. The fighting was between supporters of Hariri, a Sunni who leads the parliamentary majority, and rival followers of the Hizbullah-allied Shi'ite parliament speaker, Nabih Berri. AP contributed to this report.