The proposal failed to stop sporadic fighting on the outskirts of a commercial district occupied by protesters for six weeks as groups of demonstrators hurled petrol bombs and burned tires at two checkpoints of soldiers armed with assault rifles.
"We have agreed to take a new round of talks proposed by the Senate because if we allow things to go on like this, we don't know how many more lives will be lost," Nattawut Saikua, one of the "red shirt" leaders, told a news conference.
Several thousand protestors, who have adopted red as a protest color and broadly support former premier Thaksin Shinawatra, remain in a barricaded encampment in Bangkok's high-end shopping, hotel and diplomatic district, refusing to leave, though looking visibly worn down.
"Sure I want to go home but I want democracy first," said Chamlat Ladlao, a protester in his 50s from central Lopburi province. "I'd rather stay here, be proud and die fighting than die in my village when I'm old."
The violence had subsided considerably on Tuesday after chaotic urban warfare in the streets of Bangkok since Thursday night, following the assassination of a major-general allied with the red-shirted protesters.
Prime Minister Abhisit Vejjajiva has vowed to disperse the mostly rural and urban poor "red shirts" who accuse his government of lacking a popular mandate and colluding with Thailand's royalist elite to subvert democracy.
The government said it had no formal response to a proposal from a group of 64 senators in the 150-member upper house who have offered to mediate peace talks and urged a ceasefire.
"The prime minister has been informed but does not have an immediate position on it," said government spokesman Panitan Wattanayagorn.
Forty other senators with more pro-government leanings called on the red shirts to surrender and face criminal charges, which in some cases include the death penalty for terrorism.
"It's just the beginning and it's the kind of an offer that doesn't carry much weight since the senators are not speaking in one voice," said Somjai Phagaphasvivat, a political scientist at Bangkok's Thammasat University.
Authorities warned the red shirts to leave their barricaded encampment by Monday afternoon, but the deadline came and went, raising questions over how long the military operation would continue and whether talks would work.
Public holidays have been declared until Friday.
"I doubt the proposed talks will lead to an end to the political crisis," said Kavee Chukitkasem, head of research at stockbroker Kasikorn Securities in Bangkok.
"The government has told the red shirts to stop the protest first and then they can talk, while the red shirts asked the government to talk before they end the protests."
WOMEN AND CHILDREN
Troops have thrown a cordon around the protest site, a "tent city" at the Rachaprasong intersection, paralyzing the heart of Bangkok. Hundreds of women and children have taken refuge in a temple inside the protest area.
On the outskirts of their encampment, small groups of protesters continue to challenge the soldiers, hurling petrol bombs and stones at a checkpoint on Rama IV Road leading to the business district, and burning tires in Din Daeng, scene of intense fighting over the weekend, Reuters witnesses said.
Army spokesman Sansern Kaewkamnerd said "terrorists" have tried to stir trouble through random killings, targeting innocent people at rallies, rescue workers and journalists, including an incident on Monday in an apartment block under construction.
"A group of snipers dressed as soldiers were hiding on floors 24 to 27 aiming randomly at people, and that is being blamed on soldiers," he told a televised briefing.
Thai media reported a fire was raging in a row of deserted shops in the same area on Tuesday and firefighters were struggling to get into the area because of barricades.
Erawan Emergency Medical Center said on Tuesday that 38 people had died in the flare-up of violence since May 13 and 67 have been killed people since trouble started in April.
The protesters, mostly drawn from the rural and urban poor, and supporters of ousted ex-premier Thaksin Shinawatra, had initially demanded immediate elections.