Rival Lebanese politicians failed to bridge differences in all-party talks Thursday, but agreed to hold further discussions in efforts to try to pull the country away from a showdown between the major factions. The leaders, Christian and Muslim, pro- and anti-Syrian, met for the third time this week in a bid to ease rising political tensions that have threatened to degenerate into violence. They broke off after 2 1/2 hours and scheduled more talks for Saturday. Coming into the talks with their positions unchanged, a breakthrough appeared unlikely from the start. "The issue is complicated and sensitive. It's not that easy. Otherwise, there wouldn't be a need for such consultations," Parliament Speaker Nabih Berri told a news conference after Thursday's session. "I am not too pessimistic," said Berri, who is hosting the talks. "The most important thing is the confidence that is being rebuilt between each sides," he said. Deeply split along political and religious lines, Lebanon's many faction leaders had waged an increasingly fierce media campaign against each other, and hadn't held talks since before Hezbollah's war with Israel this summer. Berri set another round of talks for Saturday, calling on the public meanwhile not to be taken by rumors of mass demonstrations. The talks were prompted by a threat from leader Hassan Nasrallah that Hizbullah would resort to street protests to bring down the government. Nasrallah is demanding a Cabinet change, warning that failure to give his guerrilla group and its allies a veto power would prompt them to call mass protest and force early elections. Christian politician Samir Geagea insisted after Thursday's talks on his opposition to giving Hizbullah and allies concessions without discussing the fate of President Emile Lahoud, a staunch pro-Syrian who has refused to step down as pro-government factions are demanding. In previous rounds of talks earlier in the year, the leaders had failed to reach agreement on the president's fate, and anti-Syrian factions lack a large parliamentary majority to oust him. Berri, a Hizbullah ally, has said that the conference was to discuss forming a Cabinet of national unity and that there is no talk of ousting the government or the prime minister. The all-party meetings come against the backdrop of a rise in violence. Lebanon has witnessed a series of small bombings in recent weeks that have caused minor damage and six injuries. Emboldened by its ability to withstand massive attacks during its war with Israel this summer, the Syrian- and Iranian-backed Hizbullah is seeking to consolidate its political power and that of its allies to face future challenges, including international demands to disarm. The governing majority, successful in forcing Syria to withdraw its army from Lebanon last year and buttressed by recent White House support, is not willing to relinquish full control. The anti-Syrian Cabinet majority has refused to give in to the Hizbullah demand for it and its allies to have a one-third of the members of the Cabinet, a cut off figure meaning the guerrillas could effectively veto any key decision when they come to a vote in the council, where a two-thirds majority is needed. Also, a resignation of one-third of the Cabinet would automatically dissolve the council, operating only in caretaker capacity. Nasrallah has given the government until Nov. 13 -next Monday - to accept his demand. Otherwise, the highly organized group which is known to draw tens of thousands of supporters into the streets, would call mass peaceful protests against the government. But even Nasrallah's ultimatum appeared flexible for as long as the dialogue continues. Starting this weekend, some key leaders in the dialogue - Prime Minister Fuad Saniora, Berri and Christian opposition leader Michel Aoun - have scheduled trips abroad. Saniora was expected to travel to Japan, Berri to Iran and Aoun to Saudi Arabia.