The red-shirts have built large barricades in central Bangkok
Thailand's red-shirt protesters say they are prepared to join the government's reconciliation process, but they have several conditions.
PM Abhisit Vejjajiva announced the plan, which includes an offer of polls on 14 November, on Monday in a bid to end the political stand-off.
The red-shirts said they wanted a fixed date for the dissolution of parliament, and an assurance of "sincerity".
They said they would continue their protest in Bangkok in the meantime.
The red-shirts have been camped out in the Thai capital since 14 March, paralysing key parts of the city.
They say that Mr Abhisit's government is illegitimate and are demanding fresh elections.
Mr Abhisit has been under intense pressure to end the deadlock, which has forced hotels and shops to close, hitting the economy.
A red-shirt leader, Veera Musikapong, said the movement backed Mr Abhisit's proposal.
By Vaudine England, BBC News, Bangkok
The red-shirt leaders took most of a day before they felt confident in taking the stage to present a response to Mr Abhisit's "road-map" towards reconciliation.
But their message did become clear: they are eager to join a reconciliation process, they want to negotiate and they want justice for those killed during this crisis. They also refuse to accept allegations from the government that they are trying to overthrow the monarchy and say they will fight these charges.
This is not a movement that appears to be running out of steam or of negotiating tactics. The ball is now back in the government's court - will they respond with the clarity the reds demand or was the prime minister's plan a non-negotiable last chance for peace?
"We have agreed to enter the reconciliation process unanimously. We don't want any more loss of lives," he said.
But he said that the Election Commission, not the government, should set out the timeframe for the election.
And another red-shirt leader, Jatuporn Prompan, said more clarity on the poll was needed.
"We want Abhisit to come back to us with a clear parliamentary dissolution date instead of an election date and we will meet and consider it again," he said.
The red-shirts also called on the government to refrain from involving the monarchy in the conflict and cease what they called aggressive action.
The leaders said they were not seeking any amnesty for charges levelled against them but demanded that justice be administered fairly.
14 Mar: Red-shirts converge on Bangkok, hold first big rally, occupy government district
16 Mar: Protesters splash their own blood at Government House
30 Mar: A round of talks with the government ends in deadlock
3 Apr: Red-shirts occupy Bangkok shopping district
10 Apr: Troops try to clear protesters; 25 people are killed and hundreds injured
22 Apr: Grenade blasts kill one and injure 85 near protest hub; each side blames the other
3 May: PM Abhisit offers reconciliation plan and polls on 14 November
Violent confrontations between protesters and security forces since 14 March have led to the deaths of 27 people and injured nearly 1,000. Each side blames the other for the violence.
Mr Abhisit's reconciliation plan offers polls at least three months later than the red-shirts had wanted.
It also includes a call for respect for the monarchy, reforms to address social inequality, establishing a body to ensure an impartial media, an inquiry into the recent political violence and a debate on the need for constitutional reform.
The red-shirts remain camped out in central Bangkok, occupying an area stretching from the shopping district to the start of the business district.