Prime Minister Abhisit Vejjajiva proposed holding new elections on Nov. 14 in exchange for the Red Shirt protesters dismantling the camp they have set up in the middle of the Thai capital.
The Red Shirt leaders met Tuesday to discuss the five-point plan and "unanimously welcomed the reconciliation process," said Veera Musigapong, a protest leader.
He did not say, however, when they would evacuate the streets of Bangkok, and other leaders called on the government to clarify some details of the plan, including the election date.
"We want to negotiate. All of us unanimously agree that we must enter into negotiations and we want to save a lot of lives. However, we want a little bit of sincerity," said Sean Boonpracong, a protest spokesman.
The protesters said they wanted clarification on the timeframe for the election, asked for unspecified confidence-building gestures from the government and demanded the monarchy not be used as a weapon in the confrontation.
The government, in recent days, has accused the protesters of being anti-monarchy, a weighty accusation in a nation where the king is beloved and disparaging the royal family is a crime.
"Stop using the issue of overthrowing the monarchy. You are dragging (down) the institution that is loved by Thais for political reasons. Stop that," Sean said.
Abhisit made his compromise offer in a speech Monday night broadcast on all television channels, eight weeks into a tense standoff with demonstrators that has cost 27 lives.
Chavalit Yongchaiyuth, chairman of the opposition Pheu Thai party, praised the prime minister's plan and said he believes the Red Shirt protesters would end their protest Wednesday - Coronation Day, which marks the day revered King Bhumibol Adulyadej was officially crowned.
Chavalit said he expects that "all sides will cooperate to bring the country back to peace."
However, the Red Shirt leaders made no mention of any plans to end their protest Wednesday.
The protesters, mostly from the rural and urban poor, claim that Abhisit came to power illegitimately in December 2008 with the help of army pressure on legislators. They have previously called for Parliament to be dissolved in 30 days or less. An election must be held within 60 days of Parliament being dissolved.