"We have one goal, the dissolution of the house," Nattawut Saikua, a leader of the red-shirts, said.
The prime minister's concession to the about 80,000 red shirts gathered in the capital followed the news that four soldiers had been injured after grenades were thrown at an army barracks used by the government as a base during two weeks of protests.
"The blasts injured four soldiers," Major-General Prawut Thavornsiri told the AFP news agency, adding that the incident took place in the early hours of the morning.
Prawut, from the police task force monitoring the protests, said the blasts occurred near the gate of the infantry barracks on the northern outskirts of Bangkok.
The explosions were the latest in a series of more than a dozen to hit government installations.
The red shirts, loyal to Thaksin Shinawatra, the former prime minister, began their demonstrations on March 12 and have vowed they will not leave until Abhisit calls fresh elections.
Abhisit's government came to power with army backing in a 2008 parliamentary vote after a controversial court ruling removed allies of Shinawatra.
Al Jazeera's Aela Callan, reporting from Bangkok, said Abhisit's offer for talks is a "breakthrough for the protesters".
"It now appears the protesters have been able to effect some changes as far as the government is concerned," she said.
"Yesterday we saw the military pull back from several key temples where the protesters had gone."
The protesters have said that they also aimed to put pressure on the military, which has mounted a heavy security response to the demonstrations.
On Saturday, they forced soldiers across the capital to pull back from temporary postsset up to police the mass demonstrations over the previous weeks.
Nattakorn Devakula, a Thai political analyst, said the forthcoming talks with the protesters were a "a sign that [the red shirts] are gaining some ground".
He said that if the prime minister is adamant about not dissolving parliament, a key demand by the protesters, then the red shirts cannot claim victory.
"It's a partial victory so far," Nattakorn said.
He added that it would be a "loss" for Abhisit to dissolve the house "simply because protesters are out on the streets".
"Plus, I don't think he [Abhisit] is ready to win more than the half [majority] that is needed to form a ruling coalition after the election," Nattakorn said.
"The Democrats claim that they can win 240, if not 280, seats and if they're really confident they can do that, then the prime minister is probably going to be willing to dissolve the house. But deep down he knows that he cannot win the majority just yet."
Thailand has had several prime ministers since Thaksin was ousted in a coup in 2006.
Thaksin, who lives in exile to avoid a jail sentence for corruption, has regularly addressed his supporters via a videolink, raising the prospect of a campaign of civil disobedience if Abhisit continues to refuse demands to dissolve parliament.