Bangkok, Thailand (CNN) -- Anti-government protesters in Thailand say they are ready to resume negotiations if Thai authorities withdraw troops waging deadly street battles with demonstrators in the center of Bangkok.
Natthawut Saikua, a leader in the opposition United Front for Democracy Against Dictatorship (UDD), said the protesters wanted U.N.-mediated talks aimed at resolving weeks of political unrest which has seen thousands of so-called "Red Shirts" occupy an area of central Bangkok.
But a government-backed clampdown on the protesters by security forces has resulted in at least 25 deaths and hundreds of injuries since Thursday.
"We ask the government to ... withdraw troops out of surrounding area," Natthawut said. "We are ready to enter talks immediately by having the U.N. as mediator for this negotiation."
Thai authorities backed down from earlier plans to impose a curfew in Bangkok, claiming that the situation in the center of the city is under control.
Lt. General Aksara Kerdpol said a curfew was "not necessary for now," although authorities had not ruled out imposing it if circumstances changed. While allowing security forces to identify "terrorists," Aksara said a curfew would also inconvenience Thai citizens not involved in the protests.
At least one person was killed Sunday, according to hospital officials, following eight deaths on Saturday as Thai security forces declared "live firing zones" in areas of downtown Bangkok.
Earlier, another government spokesman said that protesters would have until 3 p.m. Monday (4 a.m. ET) to leave areas declared curew zones. Men would need to register before leaving, while women and children could leave without registering, Col. Sunsern Kaewkamnerd of the Center for Resolution of Emergency Situation said in a televised address.
Sunsern told reporters Sunday that demonstrators who left soon could be exempt from charges for participating in illegal demonstrations. He said officials would organize teams to enter the Rajprasong area Sunday to urge demonstrators -- especially women, children and the elderly -- to leave immediately.
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He added that soldiers had been authorized to open fire when armed people approach within a certain distance.
During his weekly televised address on Saturday, Prime Minister Abhisit Vejjajiva warned that the longer the protest continues, the higher the risk for the public.
The Red Shirts support ousted former prime minister Thaksin Shinawatra and want Abhisit to call fresh elections.
Abhisit said the government's actions were necessary to prevent Thailand from sinking into lawlessness. He said security forces and his administration are attempting to counter a small group of protesters among the opposition Red Shirts trying to foment civil war.
"The government proposed a reconciliation plan but it was rejected. This benefits no one. It only benefits a small group which wants to harm the country and lead it to civil war. It is unbelievable that they use peoples lives for political advantage," he said.
Protesters armed with slingshots and firecrackers huddled behind barricades of tires, spikes and poles Sunday. They set tires afire to create smokescreens as bullets flew around them.
Security forces rolled out razor wire and erected warning signs Saturday as they surrounded the area where the protesters have been clustered, CNN's Dan Rivers reported. He said Thai troops had also come under fire although it was unclear who was shooting at them.
"There's been quite a fierce gunfight where we are in the northwest corner of this zone that they have tried to surround a Ratchaprarop Road which has been declared a live fire zone by the army," said Rivers.
Eyewitnesses recounted stories of unarmed people being picked off. One man was shot and whisked away by emergency crews. People at the scene pointed to a building where they thought snipers were based.
"The protesters clearly blame the army for the deadly force," said CNN's Sara Sidner from the scene of the protests. "There is no way to know for sure who exactly is doing the shooting but neither of the people we saw injured were armed."
The escalating violence prompted the U.S. Embassy to issue a travel warning Saturday advising Americans to defer travel to Bangkok. The embassy will remain closed on Monday, a spokeswoman said. Several other countries, including the UK, Japan, Canada, New Zealand and the Netherlands have also advised against travel to Bangkok.
The government said it was forced to take action after demonstrators disregarded an ultimatum by Abhisit to vacate a key intersection by Wednesday.
Tensions ramped up when Maj. Gen. Khattiya Sawasdipol -- a renegade general better known as Seh Daeng, which means Red Commander -- was shot and wounded by a sniper's bullet Thursday, leaving him hospitalized in critical condition.
CNN's Sara Sidner, Dan Rivers and Kocha Olarn contributed to this report.