The authorities said they would provide buses to allow women, children and the elderly among the protesters to leave their vast protest area by 3pm (08:00 GMT) on Monday.
"Men can also leave the site but they have to show they are unarmed," Colonel Sunsern Kaewkumnerd, a spokesman for the military, told reporters.
Our correspondent said there were fears the move to get the women, children and elderly to leave was a precursor to an all out assault on the protest site.
Protest leaders told women and children with them to move to a Buddhist temple compound within their protest zone on Sunday.
The red shirts said on Sunday that they were ready to enter peace talks with the government immediately, but with the caveat that the United Nations must mediate.
"We want the UN because we don't trust we will receive justice from organisations in Thailand," Nattawut Saikuar, a protest leader, said.
"What's urgent is to stop the deaths of people. Political demands can wait," he said.
Sean Boonpracong, a red shirt spokesman, told Al Jazeera that "the situation is deteriorating to a point that if the government is smart, it's best they call off the dogs and push the army back to the base - it's getting to be a civil war".
"I don't know how the Thai government expects to have reconciliation plans while all of us are being taken prisoner," he said, adding that the red shirts were "not closing the door to peace".
But the government rejected the demand for UN-mediated talks, with spokesman Panitan Wattanayagorn saying "no governments allow any organisations to intervene in their internal affairs".
Al Jazeera's Wayne Hay reports on the continued standoff on the streets of Bangkok
The crisis appeared to be near a resolution last week when the prime minister, Abhisit Vejjajiva, offered to hold elections - a year early - in November, if the demonstrators left their protest area.
But hopes were dashed after red shirt leaders made more demands and Abhisit withdrew his offer.
The authorities say they will continue their crackdown aimed at choking off the red shirts, who have occupied a roughly 3-sq-km protest zone barricaded by fuel-soaked tyres and bamboo spikes in Bangkok's high-end shopping and tourist hub since early April.
Panitan said a pause was unnecessary since troops were "not using weapons to crack down on civilians", with the government maintaining that it is targeting only armed "terrorists" among the demonstrators.
Soldiers have encircled the core protest site and cut off utilities to the area, which itself was largely free of violence most of Sunday.
The areas between the site and the military's perimeter have become a no-man's land where gunshots and blasts can regularly be heard.
But some of the worst clashes on Sunday were behind the military cordon - an indication the unrest was not contained within the protest area and was spreading.
In one working-class neighbourhood, several hundred demonstrators gathered under an expressway overpass and in small side streets, where they sheltered between clashes with nearby soldiers.
|Protesters have used petrol bombs and other weapons against troops [Reuters]
There were also reports of scattered unrest outside the capital: a military bus was burned in the northern city of Chiang Mai and protesters demonstrated in the northeastern towns of Nongkhai and Udon Thani to defy the government's state of emergency, which bans gatherings of more than five people.
The decree, which gives the army broad powers to restore order, was extended on Sunday to 22 of Thailand's 75 provinces, up from 17.
Along with the expanded state of emergency, the government also ordered schools to remain shut on Monday and declared two days of national holidays to keep civilians off the streets.
The army put off a plan to impose a curfew in parts of the city but did not rule out restricting night-time movements if the situation worsened.
In the early hours of Monday morning, guests at the Dusit Thani hotel, which overlooks the red shirts' encampment, were evacuated to the basement after the building came under gunfire and was rattled by an explosion.
Guests were later allowed back to their rooms but the hotel said in the morning that it was closing for fear of more attacks.
Fire gutted three commercial buildings in another area and Australia became the latest country to shut its Bangkok embassy due to the "ongoing violent clashes", after the US and Britain closed theirs.
Appeal to king
Days of prolonged fighting and disruption to normal life have taken their toll on 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 city's two mass transit train lines remain closed and those wanting to travel in the city often have to take long detours to avoid deadly "no-go" zones.
Jatuporn Prompan, one of the red shirt leaders, urged the country's revered king to intervene in the crisis on Sunday, saying he was the "only hope" for an end to the two-month-old crisis.
"I believe Thais will feel the same, that His Majesty is our only hope," Jatuporn told reporters at the rally site, where 5,000 protesters remained camped, nearly half their number in recent days.
In a 1992 uprising, King Bhumibol Adulyadej chastised the military and protest leaders, bringing the violence to an end. But he has so far not publicly commented directly on the ongoing crisis.