Rachel Harvey has some analysis for the BBC:

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.

AFP:

Political analyst and Thaksin biographer Chris Baker predicted a lengthy stand-off and questioned the strength of support for Abhisit among the political elite.

“How do the military and various other people think they can best manage the situation? I think they’re likely to think Abhisit’s quite simply expendable,” he said. “I don’t think these talks will be over so quickly.”

Thomas Fuller in the NYT:

The meeting, an unscripted and unusual face-off between hardened political rivals that was broadcast live on Thailand’s main television channels, failed to make progress on the main demand of protesters, that new elections be called. Both sides agreed to meet again Monday.
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Mr. Abhisit, looking uncomfortable at times, said he would “make a decision based on a consensus from the entire country” and questioned whether calling for new elections would solve the country’s four-year-old political crisis.
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The three protest leaders were generally cordial in the televised meeting Sunday, patiently jotting down notes when the Prime Minister spoke, a contrast to the fiery speeches they have given in recent weeks when they denounced Mr. Abhisit as a puppet of the elite and military. In contrast to the raucous street rallies, the meeting room was quiet enough to hear water being poured. Attendants brought snacks and hot drinks.

AP:

Thai Prime Minister Abhisit Vejjajiva and leaders of anti-government protests failed to reach an agreement Sunday in nationally televised talks on how to solve the country’s political crisis and said they would try again the next day.

The talks marked a civilized pause 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. With strained smiles, they reiterated their sharply different stances and adjourned three hours later no closer to a resolution. They agreed to meet again Monday evening.

“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 leaders, all dressed in their signature red shirts.

A tense-looking Abhisit — accompanied by two advisers, all wearing blue dress shirts — reiterated his position that dissolving Parliament immediately would not solve Thailand’s deep political crisis.

AP again with some post-talk comments by the red shirts:

“For now, we are not going to mobilize any more red shirts,” protest leader Jatuporn Prompan said as he exited the talks. “But we hope that tomorrow we get a clearer picture.”

Sunday’s talks gave the Red Shirt leaders new legitimacy but offered a face-saving situation for both sides, analysts said.

“The prime minister has defused the tension quite nicely,” said Somchai Pagapasvivat, political science professor at Bangkok’s Thammasat University.

“The meeting today and tomorrow won’t achieve anything concrete. But it’s a truce. It’s a temporary win-win situation for both sides,” he said. “There’s no exit now, but in the future it will depend on who can garner more support.”

Reuters mainly focuses on what Abhisit said, but also notes that the red shirts had began to up the ante in the days before the talks. Key excerpt:

He smiled and promptly concluded the talks after one leader, Jatuporn Prompan, asked him to dissolve parliament within two weeks. “I don’t think we need to have ultimatums or deadlines,” Abhisit said.

“I’m willing to have more talk like this, hopefully a second round, a third round and you can protest all you want. If we try to draw a dividing line, things will not be over,” he added.

After two weeks of peaceful rallies, the “red shirts” have stepped up their campaign to topple the government with a new level of brinkmanship that has raised tension and stoked fears of clashes between demonstrators and security forces.
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They stepped up the protest tempo two days after Thaksin, the ousted, exiled premier who is assumed to be their leader and financier, called for a campaign of “civil disobedience.”

The Times (UK):

The meeting with Mr Vejjajiva represents a tactical victory for the Red Shirts who appeared a week ago to be on the back foot after falling short of the one million protesters that they had promised to bring to Bangkok. But tens of thousands of people, many of them poor farmers from the country’s north and northeast, held on.

BP: Do agree that it is a victory of some sorts for the red shirts, but as noted above also think that Abhisit comes out of this looking good as he has defused tensions. Abhisit cannot give in completely and will need to extract at least a delayed dissolution otherwise he will look weak if he gives in to everything now. The red shirts also have to compromise and that means a temporary halt in increasing the protest size which could weaken the UDD momentum. They will also have to explain any compromise to their supporters and that can deflate the protest enthusiasm.