Face-to-face talks between the Thai PM and protesters who want his resignation and new elections have been adjourned, with a new round due on Monday.
A spokesman for Abhisit Vejjajiva said he had accepted the offer of talks in an effort to "restore peace and minimise the chance of violence".
His meeting with the protest leaders was broadcast live on Thai TV.
Correspondents say the talks are a sign of compromise after two weeks of demonstrations in the capital, Bangkok.
I have to make a decision based on a consensus from the entire country, not just the Red-Shirts
Abhisit Vejjajiva Thai Prime Minister
During the protests, the prime minister consistently said he would not bow to any ultimatums.
Earlier, four soldiers were injured after grenades were thrown at a heavily guarded army barracks on the outskirts of the city, which Mr Abhisit has been using as a base.
It is not known who carried out the attack, but the Red-Shirts - a loose coalition of left-wing activists and supporters of exiled former Prime Minister Thaksin Shinawatra - had been due to march there on Sunday.
Mr Abhisit went on television on Sunday morning to say he was open to negotiations, but insisted he would "not there be there to talk" if the protesters proceeded to march on the barracks.
Rachel Harvey, BBC News, Bangkok
There were handshakes and smiles and a good deal of respectful listening but ultimately no change in well-entrenched positions.
The anti-government protest leaders, dressed in their trademark red shirts, repeated their demand for new elections. This, they said, was the only way to solve the problems created by the military coup of 2006.
But the prime minister countered that in his view an early poll could inflame an already volatile situation. So no obvious meeting of minds, but there has been a shift in the political dynamic here.
After months of portraying the protestors as merely a proxy for exiled Prime Minister Thaksin Shinawatra, the government now appears to be treating the Red-Shirts as a legitimate political movement and that will not have been lost on the many Thais watching the discussions live on television.
"It will not be possible under this kind of tense circumstance to hold negotiations," he said. "I still insist that I am open to negotiation as long as there are no threats, hostility or pressure."
Red-Shirt leader Nattawut Saikua subsequently delayed the rally, saying he wanted to give the government time to consider an offer of negotiations between small delegations.
The meeting was held at an academic research institute in Bangkok, deemed to be a neutral venue.
Sitting across a conference table from each other, the two teams of three representatives shook hands and then listened politely while the others set out their positions.
Veera Muksikapong, a member of the Red-Shirt delegation, stated that the movement respected Mr Abhisit as an individual, but then repeated their demand for fresh elections.
"Our request is simple and direct: dissolve parliament for the people to decide again," he told the prime minister.
Mr Abhisit, flanked by two trusted aides, questioned whether calling elections would ease tensions or exacerbate them.
"I have to make a decision based on a consensus from the entire country, not just the Red-Shirts," he said. "We have to think: will dissolution really solve the problem?"
2006: Yellow-shirts launch street protests to oust PM Thaksin Shinawatra
Sept 2006: Thaksin ousted in military coup
Dec 2007: Thaksin allies win first post-coup elections
Sept 2008: Yellow-shirts occupy Bangkok government buildings, clash with pro-Thaksin red-shirts
Nov 2008: Yellow-shirts occupy Bangkok's airports, forcing cancellation of hundreds of flights
Dec 2008: Thaksin-allied government falls, rival Abhisit Vejjajiva forms government
Apr 2009: Red-shirts storm Asean summit, clashes erupt in Bangkok
Mar 2010: Red-shirts launch protest aimed at bringing government down
The talks come a day after tens of thousands of protesters forced soldiers to move away from several key locations in the capital, where they had been deployed under special security legislation.
On Thursday, Mr Thaksin called for a campaign of "civil disobedience".
The Red-Shirts, formally the United Front for Democracy against Dictatorship, have sought to distance themselves from Mr Thaksin - who lives abroad having fled a two-year jail sentence for a conflict of interest case - painting themselves as fighters for democracy.
They say Mr Abhisit came to power illegitimately in a parliamentary vote after a pro-Thaksin government was forced to step down. Mr Thaksin was ousted as prime minister in a military coup in 2006.
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