The reds protesters have demanded justice for civilians killed in the April 10 bloodshed by bringing all those responsible to justice, red-shirt leader Natthawut Saikua said.
"We agree to end the protest after Suthep turns himself in to authorities to take responsibility for the death of 20 civilians in the clash," he said.
The red-shirt leaders said they were also prepared to surrender themselves to police.
"Once Suthep actually turns himself in, we will end the protest and do like him," Natthawut said.
Suthep, as head of the Centre for the Resolution of the Emergency Situation (CRES), instructed security officials to remove protesters from the Phan Fah Bridge. The operation exploded into violence, with protesters resisting and mysterious gunmen shooting at officials and firing grenades.
The protesters accuse the authorities of using live bullets with the intention of killing, while the government alleges the red-shirt leaders committed terrorist acts.
Deputy PM Suthep bows to red-shirt demand, will surrender to the DSI this morning over April 10 clashes; Abhisit says he'll do the same when his immunity expires at the end of the parliamentary session late this month