Thai Prime Minister Abhisit Vejjajiva and leaders of anti-government protests have failed to reach agreement on how to solve the country's political crisis and say they plan to meet again Monday. The two sides held three hours of nationally televised negotiations Sunday. Abhisit's office said the prime minister agreed to meet the protest leaders to restore peace and minimize the chance of violence. Protests that started March 12 have turned increasingly confrontational, raising fears of violence. The protesters are mainly supporters of ex-leader Thaksin Shinawatra, who was deposed in a 2006 military coup. They say Abhisit took power illegitimately and are demanding he dissolve Parliament and call new elections. After weeks of demonstrations and fiery rhetoric that prompted Abhisit to seek refuge at an army base, the two sides sat across a conference table from each other and shook hands. They then reiterated their sharply different stances. “Our request is simple and direct: Dissolve Parliament for the people to decide again,” said Veera Muksikapong, a protest leader. He was joined by two other protest leaders, all dressed in their signature red shirts. A tense-looking Abhisit – accompanied by two advisers, all wearing blue shirts –reiterated his position that dissolving Parliament immediately would not solve Thailand's deep political crisis. “I have to make a decision based on a consensus from the entire country, including the Red Shirts,” Abhisit said. “We have to think: Will dissolution really solve the problem?” Abhisit has repeatedly rejected the protesters' demands that he dissolve Parliament and call new elections. Thousands of protesters gathered in the historic heart of Bangkok awaiting direction from their leaders on how to respond if the talks failed. During more than two weeks of protests, the number of participants has peaked at more than 100,000. The protest movement consists largely of supporters of Thaksin, who was ousted by a 2006 military coup for alleged corruption, and pro-democracy activists who opposed the army takeover. Protest leaders have increasingly portrayed the demonstrations as a struggle between Thailand's impoverished, mainly rural masses and a Bangkok-based elite impervious to their plight. Thaksin's allies won elections in December 2007, but two resulting governments were forced out by court rulings. A parliamentary vote brought Abhisit's party to power in December 2008, leading the Red Shirts to complain his rule is undemocratic. The protesters issued an ultimatum Sunday threatening to scale the walls of the army base where Abhisit has been staying unless he agreed to meet them face-to-face. Abhisit went on national television earlier in the day saying he would not bow to ultimatums. Two hours later, however, he agreed to the talks. “To find a way to restore peace and minimize the chance of violence, the prime minister has accepted the condition to negotiate with the protesters,” a member of Abhisit's staff said in a brief announcement. The two sides met at an academic institute on the outskirts of Bangkok. Security officers searched the venue for bombs before Abhisit entered. Four Thai soldiers were wounded early Sunday when two grenades were fired into the army barracks at the 11th Infantry Regiment that is serving as Abhisit's base, Thai media reported. – AP More than a dozen explosions have hit government targets since the protests began, including attacks on two television stations and the customs department on Saturday that wounded at least eight, according to the Thai News Agency. Abhisit has called in thousands of troops to guard Parliament, government buildings and other key locations. Protesters have denounced the show of military force as unfitting for a democracy.