The Thai government has said it will accept a ceasefire offer from a leader of the so-called red shirts movement if the protesters return to their camp in central Bangkok.
Nattawut Saikuwa called Korbsak Sabhavasu, the government's chief negotiator, on Monday, the first direct contact between the two sides since bloody clashes that have left at least 37 people dead started on Thursday.
Korbsak told reporters that he talked to Nattawut for five minutes, during which the red shirt leader proposed a ceasefire.
He said he told Nattawut that the army will stop shooting if he calls his fighters back from the streets to the main encampment where they have been living.
"If they call their people back to Rajprasong there will be no single bullet fired by the soldiers,'' Korbsak said, referring to the three sq km protest area in a commercial district of the capital.
The Rajprasong area is encircled by troops, and protesters have spilled out into surrounding streets that have become a battleground.
Protesters have set fire to vehicles and fired homemade bombs and firecrackers at the soldiers, who have responded with live ammunition.
On Monday at 3pm local time, a Thai government ultimatum passed for the estimated 5,000 protesters occupying Rajprasong to leave the site or face up to two years in prison.
But the protesters, including 400 elderly and children taking refuge at a temple, stayed in the barricaded area.
"We will keep sending warnings to protesters and will slowly step up pressure if they don't go," Thawil Pliensee, the secretary-general of the National Security Council, said.
He said the military had no immediate plans to clear the main camp by force.
The government had offered to provide buses to take the protesters home if they left voluntarily, but some protesters said they refused to board a government bus for fear they would be arrested.
Al Jazeera's Wayne Hay, reporting from Bangkok, said some protesters might also be hesitant to leave because they fear retaliation from protest leaders.
"The leaders have been on stage and told the supporters 'you're free to go, we're not holding you inside this area, if you feel you're in danger you're free to return home'," he said.
"But we've heard reports that some of those supporters, while they may want to go home, feel a bit uneasy about catching one of the government buses because they feel that they may face some kind of recrimination from the red shirts."
Earlier on Monday, a key military strategist of the red shirts died in a Bangkok hospital.
Major-General Khattiya Sawasdipol, better known as Seh Daeng or Commander Red, had been accused by the government of being a renegade soldier and creating a paramilitary force for the so-called red shirt protesters.
His death came after he was shot in the head - reportedly by a sniper - while talking to journalists inside the perimeter of the protest zone on Thursday.
|A key red shirt leader was buried on Monday after being shot in the unrest [Reuters]
About 1,000 people attended a funeral for the slain general at a pagoda in the city's historic district.
Days of fighting has disrupted the lives of many of Bangkok's 12 million residents.
Most shops, hotels and businesses near the protest area are shut and supermarkets outside the protest zone have seen long lines as people rush to stock up on supplies.
The government has ordered schools not to reopen after summer holidays, and has declared two days of national holidays to keep civilians off the streets.
Al Jazeera's Aela Callan, reporting from the centre of Bangkok, said the unrest was having a "huge impact" on the city, with the military zone stretching another 5sq km beyond the protest site.
"It's quite a significant portion of Bangkok that has been cordoned off," she said.
"People are very much staying indoors, not going to their offices as normal and those who are finish very early in the afternoon, before nightfall. Public transport isn't working as it usually is."