Red-shirt protesters have occupied central Bangkok for weeks
Thailand's red-shirt leaders say they will continue their weeks-long protest in Bangkok unless certain conditions are met.
The red-shirts accepted PM Abhisit Vejjajiva's offer of 14 November polls but said they would not go home until the deputy PM surrendered to police.
They say Suthep Thaungsuban must answer for the deaths of protesters in a 10 April clash.
Mr Abhisit had given the red-shirts a Monday deadline to respond to his plan.
Both the ruling elite and the red-shirts are divided over how to end the protests.
Mr Abhisit's reconciliation plan includes holding elections in November and so dissolving parliament in mid-September.
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
At a news conference, the red-shirts said they broadly accepted the timeframe laid down in the road-map.
But they said that they wanted to ensure there were no double standards in the repercussions before agreeing to close down their protests.
They said many of their members had been accused of terrorism or been subject to arrest warrants, so Mr Abhisit and Mr Suthep should be subject to the same scrutiny.
Mr Abhisit has parliamentary immunity but Mr Suthep should surrender to police to face accusations of murder, they said.
Mr Suthep was in charge of security operations on 10 April, when 25 people were killed in a failed attempt to disperse protesters. His role was subsequently given to army chief Gen Anupong Paojinda.
"If Suthep refuses to surrender himself to police, we refuse to end the rally," red-shirt leader Nattawut Saikua told reporters. "If Suthep surrenders to police, then we will go home."
A government spokesman says the deputy prime minister will meet the head of special investigations on Tuesday to hear the accusations levelled against him.
But the BBC's South East Asia correspondent, Rachel Harvey, says it is not clear whether or not this is in response to the protesters' demands or part of a complex deal that has been rumoured to be in the offing for days.
Thousands of protesters remain in camps along major thoroughfares in the centre of Bangkok.
Two policeman were killed in the city over the weekend, bringing the protests' toll to 29.
The prolonged demonstration has forced the closure of shops and hotels and led to a sharp drop in the vital tourism industry.
Over the weekend reinforcements from the northeast of Thailand arrived at the protestor's camp, swelling numbers which had recently appeared to be dwindling.
The protestors, a loose coalition of left-wing activists, democracy campaigners and supporters of ousted leader Thaksin Shinwatra, say the government is illegitimate because it came to power through a parliamentary deal rather than an election.