Abhisit, who has spent most of the eight-day-long rally in an army barracks due to security fears, said on Sunday that he would not meet the protesters immediately.
"They can talk to me but before reaching that step, they must meet representatives to talk about the outline of talks," he said on his weekly television programme.
"If [the red shirts] come it means they are interested in democracy. If not, they are following what Thaksin [Shinawatra, the former prime minister] wants them to do."
Abhisit had said earlier the demonstraters had agreed to send two senior red shirts to meet one of his ministers and a government official for talks on Monday arranged by senators.
But after their colourful convoy returned to the main rally site in the Thai capital, Bangkok, on Sunday, the red shirts stuck to their demands for snap polls.
The red shirts - formally known as the United Front for Democracy against Dictatorship - say the current government is illegitimate as it came to power with army backing via a December 2008 parliamentary vote after a controversial court ruling removed Thaksin's allies.
In what they have increasingly dubbed a "class war", the mainly poor and rural red shirts say they are fighting Thailand's elite in bureaucratic, military and palace circles, whom they accuse of ousting elected governments.
Buoyed by a huge parade, the defiant red shirts said on Sunday they would paint a white canvas with blood left over from the gallons donated by supporters and splattered on the prime minister's house and offices over the past week.
"We will depict our fighting in poems and paintings," Visa Kantab, one of the red shirts, told the red-clad crowd gathered at their main rally site in Bangkok's old quarter on Sunday, the eighth day of their protest.
"After we have finished, we will display our artwork on the stage, and after we are victorious, we will frame it as evidence of history," he said.
Saturday's carnival-like protests, which swelled to 65,000 people, aimed to recruit urban support and revive their waning rally demanding the dissolution of parliament and immediate elections.
But a few hours after the parade, two small explosions hit Bangkok and a nearby province, targeting a new National Counter Corruption Commission office and a road near the defence ministry.
It was not clear who was behind the suspected grenade attacks, in which one person suffered minor wounds, police said.
Thaksin, who lives in exile to avoid a jail term for corruption, spoke to supporters via videolink on Saturday night, thanking those who took part in the parade. "I'm really proud of you. I almost cried," he said.
"Today I want to invite everyone to join us to call for democracy. You don't have to wear red, but just have one ideology: Democracy," the former premier, who was deposed in a coup in 2006, said.
A 50,000-strong security force has been in place in Bangkok and surrounding areas during the protests under a strict security law, which is in place until Tuesday but may be extended until a later date if rally goes on, Abhisit said.
Thailand has been rocked by protests since Thaksin's removal from power by both his supporters and his opponents, many of whom are in Bangkok and accuse him of corruption and of disloyalty to the revered royal family.