But he later condemned the protests, saying the demonstrators had broken the law. But he said the government would continue its policy of tolerance to avoid violence.
"We are working to ensure that the country returns to normal as soon as possible," he said in a televised address.
"We are confident we can use the law to resolve the problem."
'Ready to fight'
Leaders of the red shirts movement had earlier said that they would call off marches planned in parts of the city after briefly scuffling with soldiers and riot police attempting to block them.
But protesters later confronted riot police on Ratchadamri Road, near the city centre, pelting them with eggs and water bottles, before breaking through the blockade.
Protest leaders said they planned to stage convoys through 11 of the capital's main roads that the government has declared off-limits to them.
The red shirts have also defied government orders to leave the city's commercial district, vowing to push ahead with their demands for Abhisit to stand down and call new elections.
Earlier red shirt leaders had threatened to "break every checkpoint" in Bangkok in a bid to topple the government.
"We are ready to fight and die here," Nattawut Saikuar, a red shirt leader said on a rally stage.
"The government put pressure on us, but we are staying put. Now we will retaliate with our own offensive."
Then for a while tensions appeared to ease with an announcement that the red shirts had called off their marches, saying instead that they would remain in Rachaprasong, Bangkok's main shopping district, for a fourth day.
In response riot police and soldiers – who had been deployed across Bangkok in the hundreds - were pulled back, although they continued to surround the main protest site.
But later in the day scuffles broke out as protesters moved again to break through police lines, saying the planned marches were back on.
'Right to protest'
Sean Boonpracong, a red shirts spokesman, told Al Jazeera that the government had no justification to disperse the protesters.
|Business leaders have said the protests could do lasting damage to the economy [Reuters]
"It is our constitutional right to protest and no one is afraid of this government anymore," he said.
Many of the red shirt protesters are supporters of Thaksin Shinawatra, the former prime minister, who was ousted in a 2006 military coup.
Abhisit has offered to call elections by December, a year ahead of schedule, but the protesters have said they want to see action much sooner.
The red shirt movement - known formally as the United Front for Democracy Against Dictatorship - contends that Abhisit, who became prime minister in December 2008, came to power illegitimately.
The protests have caused widespread disruption in the Thai capital and business leaders have warned that unless the crisis is brought to a swift end it will inflict lasting damage on the economy.
More than a dozen malls in one of Bangkok's top shopping districts have been forced to close as a result of the protests, with many nearby hotels reporting an exodus of tourists.