BANGKOK – The Thai government said Monday it would accept a cease-fire offer from a “Red Shirt” protest leader if their fighters end raging street battles and return to their main camp in central Bangkok, as the death toll from five days of violence rose to 37.

The offer was made by Red Shirt leader Nattawut Saikuwa, who called the government’s chief negotiator, Korbsak Sabhavasu, on his cell phone, Korbsak said. The conversation was the first direct talks between the two sides since the fighting started Thursday, but Korbsak said it was unlikely to achieve much, as the sides remained far apart.

Nattawut’s response was not immediately known. Calls to his phone went unanswered.

Earlier, a Thai government ultimatum passed for the thousands of protesters — who have been camping in an upscale commercial district for more than a month in a bid to force the government from power — to vacate the barricaded protest zone by 3 p.m. or face up to two years in prison.

Meanwhile, unrest flared in various parts of the downtown area outside the barricades, as troops fired live ammunition at protesters who were lighting tires to hide their positions. The thick smoke darkened the sky.

The Red Shirts, many of whom come from the impoverished north and northeast, are trying to unseat Prime Minister Abhisit Vejjajiva and force immediate elections.

They say the coalition government came to power through manipulation of the courts and the backing of the powerful military, and that it symbolizes a national elite indifferent to their plight.

Previous attempts to negotiate an end to the standoff — which has destabilized a country once regarded as one of Southeast Asia’s most stable democracies — have failed. A government offer earlier this month to hold November elections floundered after protest leaders made more demands.

Korbsak told reporters that he talked to Nattawut for five minutes, during which the Red Shirt leader proposed a cease-fire. He said he told Nattawut that the army will stop shooting if he pulls his fighters back from the streets to the core protest site.

“If they call their people back to Rajprasong there will be no single bullet fired by the soldiers,” he said,.

“If he (Nattawut) is serious about solving the problem, he is capable of doing it. He can simply call back his people. Once he calls them back who would the troops shoot at?” Korbsak said.