The Criminal Court ruled on Monday that Phan Khamkong, a taxi driver from Yasothon, was shot and killed on May 15, 2010 by troops acting on orders issued by the Centre for the Resolution of Emergency Situations (CRES).
Mr Suthep was CRES director at the time.
Mr Tarit said the ruling would be a precedent for the courts to proceed with the 35 other cases involving deaths during the 2010 riots. All concerned should accept the ruling, he said.
The DSI chief said it was possible that Mr Abhisit and Mr Suthep could be charged with premeditated murder under articles 288 and 289 of the Criminal Code because they were ultimately responsible for ordering the military to quell the riots.
The soldiers who honestly performed their duty were entitled to protection by Article 70 of the Criminal Code.
There were two possible options, he said. One, they could be charged, but not prosecuted. Two, they could be prosecuted, but excluded as witnesses.
However, whether legal action would be taken against anyone and on what charges was still to be decided by the committee investigating the deaths of 91 people during the violence, Mr Tarit said.
The Criminal Court ruled on Monday that government forces were responsible for the death of taxi driver Phan.
Basing its decision on testimony from witnesses and examination of other evidence, the court found that Phan was hit by bullets fired by soldiers who were shooting at a van driven by Samorn Maithong near an airport rail link station on Ratchaprarop road. The troops were ordered to that position by the CRES.
It was concluded that the soldiers' gunfire killed Phan and wounded Mr Samorn.
The court ruled that Phan's death was caused by government troops.
The prosecution will now include the court ruling in its case report on its investigation of his death, which will be handed over to the DSI for further inquiries and possible action.