The deaths, in police custody at Tak Bai in Thailand's restive south, sparked a spate of attacks and counter measures by the authorities.
Shinawatra, attending a gathering of the Association of South East Asian Nations (Asean) in Laos, at first praised his forces for their handling of the protest, while rights groups and witnesses accused the government of heavy handedness. No one has yet been held responsible for the massacre.
In the latest violence an army officer and a suspected separatist were killed in the mainly Muslim south of the country where activists are campaigning for more power and better rights.
Sergeant Prapan Northong, 43, was shot dead on Monday in what appears to have been a drive-by shooting as he was taking his two children to school by motorbike in the province of Pattani, according to a police spokesman. The children were unharmed.
"The victim, who was attached to Pattani army headquarters, was shot dead at 6.45am as he drove his children to school. He died instantly at the scene," the spokesman said.
The shooting came a few hours after Muktar Kureng, 28, was shot dead in an exchange of fire with police and military in Pattani after his car failed to stop at a checkpoint, police said.
Rights groups have accused the
police of heavy handedness
Another man in the car fled during the shootout at 12.30am on Monday and police said they discovered six assault rifles, grenades and bombs inside the vehicle.
Police also said they believed dissidents were moving the weapons to launch an attack on targets in the neighbouring province of Narathiwat.
"The victim was on a wanted list," a police spokesman said.
The approximately six million Muslims of Thailand's south have been hard hit by what the government says are counter measures to curb an insurgency, with Muslim groups saying they are the victims and are being used as scapegoats by both the government and criminals.
Narathiwat Islamic council president Abdul Rahman Abdul Samad said Muslims felt like immigrants in their own homeland, powerless to influence events.
The council feels its call for restraint and understanding has fallen on deaf ears, Abdul Rahman said.
"We need things done peacefully, but it has only been violence and cruelty dished out so far," he said.