Bangkok, Thailand (CNN) -- Thai Prime Minister Abhisit Vejjajiva will meet Monday with the leaders of an anti-government movement for a second day of talks after their first session failed to produce an agreement.
The opposition -- members of the United Front for Democracy Against Dictatorship, or UDD -- is demanding that the prime minister dissolve the parliament within two weeks.
Jatuporn Prompan, one of the party leaders, said he wanted an answer from Abhisit at the Monday meeting.
Those talks are scheduled for 6 p.m. (7 a.m. ET) and, like Sunday's face-to-face discussions, will be carried live on television.
The government said in a statement Monday that Abhisit has not ruled out a dissolution of parliament, but the timing and other matters have to be discussed first.
"Despite the threat to elevate the level of demonstrations to a higher level if the negotiations do not succeed, the government is still optimistic and believes that having negotiations is the right approach," the statement said.
The "red shirts" -- so named for their clothing -- have amassed by the thousands in central Bangkok and have said they will not leave until Abhisit calls fresh elections.
Abhisit agreed to the talks after the protesters pulled back their crowd from outside the army's 11th infantry regiment headquarters, where he has been staying.
At Sunday's talks, Jatuporn bluntly asked Abhisit whether he would dissolve parliament.
"If you don't, we will just go back to the street and continue our demonstration," he said.
The prime minister said the "polarization problem" had deepened too far to be solved by just dissolving parliament.
The protesters are supporters of former Prime Minister Thaksin Shinawatra, who was ousted in a bloodless military coup in 2006. Thaksin was the only Thai prime minister to serve a full term and remains hugely popular.
He fled the country in 2008 while facing trial on corruption charges that he say were politically motivated.
The protesters say Abhisit was not democratically elected and have demanded that he call elections.
Two people were killed and at least 135 wounded in riots in April when protesters clashed with demonstrators supporting the government.