"We want the UN to moderate it because we do not trust anyone else. There is no group in Thailand that is neutral enough."
Nattawut said the red shirt leadership would recall protesters who had been sent out to challenge the army if the conditions were met.
'No conditions accepted'
At least 29 people have been killed and more than 200 others wounded in four days of violent unrest in Bangkok.
The government's immediate response to Nattawut's statement was that no conditions should be attached to negotiations.
"If they really want to talk, they should not set conditions like asking us to withdraw troops," Korbsak Sabhavasu, the prime minister's secretary-general, said.
"It's a positive sign but if there is going to be a talk, there has to be more detail. But they cannot make demands if they want to negotiate."
Al Jazeera's Wayne Hay reports on the continued standoff on the streets of Bangkok
The red shirts are demanding the resignation of Abhisit Vejjajiva, the prime minister, and early elections.
Sean Boonpracong, a red shirt spokesman, said the protesters were surrounded by security forces a little after midnight local time (1600GMT on Sunday).
"This is not only taking place in Bangkok, but all over the country, in many provinces," he told Al Jazeera.
"The situation is deteriorating to a point that if the government is smart, its best they call off the dogs and push the army back to the base.
"It's getting to be a civil war. However, we are not closing the door to peace. I don't know how the Thai government expects to have reconciliation plans while all of us are being taken prisoner."
Earlier on Sunday, the government moved back from an announcement that it would impose a curfew in Bangkok, saying it was no longer necessary and would be an inconvenience.
"It is not yet necessary to impose the curfew even though it would help the authorities to differentiate people from terrorists," Lieutenant-General Aksara Kerdphol said.
Intense clashes took place in the city on Sunday afternoon.
A grenade was tossed at troops in the Bon Kai area, who responded with gunfire that scattered the demonstrators into nearby alleys, witnesses said.
The red shirts camouflaged themselves behind barricades of burning tyres.
The government said Monday and Tuesday would be public holidays in Bangkok.
The military has declared certain areas of the city to be "live fire zones", which means security forces are permitted to use live ammunition against protesters trying to enter these areas.
Plumes of smoke
Al Jazeera's Wayne Hay, reporting from Bon Kai, one of the "live fire zones", said troops were facing off with several hundred red shirts who had built barricades and blocked access to the area.
"The red shirts are lighting tyres and there are large plumes of smoke ... This is definitely red shirt territory," he said.
"The soldiers are firing live rounds. They're firing horizontally towards the protesters through the smoke.
"It's very difficult to see what they're firing at but at times you can see red shirts supporters dashing around across the road launching their own projectiles towards the troops."
The army has cautioned that it would move against the demonstrators' main rally site unless they dispersed, although it gave no timetable for any such action.
Al Jazeera's Aela Callan, reporting from the main protest site on Sunday, said the protesters showed no signs of giving up.
"There's a hardcore group of several thousand red shirts who are saying they won't budge," she said.
"They're really hunkered in there, they've set up their homes. They've been there for a very long time.
"Some of the red shirts I have spoken to have said they're not willing to leave, they're not scared."
As soldiers opened fire on demonstrators, they responded with sporadic attacks on the army's positions, using petrol bombs to torch vehicles.
More than 50 people have been killed and 1,600 wounded since the protests began on March 12, according to figures from the emergency services and the public health ministry.
Razor wire fortification
For the last two months, thousands of protesters have turned a large area of Bangkok into a virtual city within a city, crippling a retail and hotel district and disrupting daily life for residents in the city of 12 million people.
The rally site, where demonstrators sleep on mats on the ground and listen to speeches and music blasted from giant speakers, stretches for several square kilometres.
It is fortified with razor wire, bamboo sticks and piles of tyres.
The mostly poor and working-class red shirts say the government is elitist and undemocratic because it came to power in a 2008 parliamentary vote after a court ruling ousted the elected allies of Thaksin Shinawatra, a former prime minister.
Protest leaders have also called for the intervention of Thailand's revered King Bhumibol Adulyadej.
But the monarch, seen as a unifying force, has been hospitalised since September and has avoided commenting directly in public on the crisis.