The case involved the deaths of Phan Khamkong, a 43-year-old taxi driver from Yasothon and Kunakorn Srisuwan, a 14-year-old boy, near Airport Rail Link's Ratchaprasong station on May 15, 2010.
It also involves the injuries of Samorn Maithong, a van driver, on Ratchaprarop road.
The Criminal Court earlier ruled that the deaths and injuries were caused by military gunfire ordered by the Centre for the Resolution of the Emergency Situation (CRES) under the command of Mr Abhisit and Mr Suthep.
The court set today for the examination of evidence.
The lawsuit was read to Mr Abhisit, who denied the charges.
The court also raised for consideration a request by Mr Samorn and Mrs Noochid, Mr Phan's wife, to be co-plaintiffs in the case. Mr Abhisit had no objection.
The former prime minister told the court the National Anti-Corruption Commission (NACC) is still in the process of investigating into his involvement in the crackdown.
He said he had testified to the NACC, but the NACC has not concluded the investigation. Mr Abhisit added that the NACC had also asked for an investigation report of the Department of Special Investigation (DSI) to complement its own inquiry.
The court agreed to send a letter to the NACC to ask for its findings.
The court subsequently ordered the postponement of the examination of evidence to June 23 from 9am.
Mr Abhisit refused to talk to the press after the hearing was over.
Bundhit Siriphan, his lawyer, said if the NACC finds Mr Abhisit not guilty in performing his duty as prime minister, the finding would be used in Mr Abhsit's defence in the Criminal Court.