
Among top police officers at the meeting were General Thani Somboonsap and Lt General Aswin Kwanmuang.
"I want law enforcement authorities to quickly resolve cold [long term unsolved]cases with consequences on human rights and violence in the deep South so as to stop the problems from festering," Abhisit said.
He said his government would fully back the investigative proceedings in order to uphold the law.
The country's reputation will be mired so long as the cases remain unresolved, he said.
"The prime minister has instructed police to devote full attention to four or five unsolved cases which have implications for security and international affairs," Aswin said.
The cases included the mysterious disappearance of human rights lawyer Somchai Nilaphaijit, the murder of an English couple in Hua Hin and the killing of a state witness involved in the Somchai case.
Aswin said police would work closely with the Department of Special Investigation to solve the cold cases which have already been placed under the jurisdiction of the DSI.
He also dismissed speculation he was a top contender to replace DSI director general Thawee Sodsong, seen as close to the pro-Thaksin camp. He said he wanted to continue working in the police service.
Thani said some progress was being made on the Somchai case although it is still too early to anticipate whether culprits could be apprehended and brought to justice.He said the government did not set a deadline for getting the job done.
Justice Minister Pirapan Salirathavibhaga said the DSI, which is under his supervision, was under a firm instruction to clear the backlog of cold cases, including the unsolved killings impacting Thai-Saudi relations.
A number of cases will reach the statute of limitations by next year and the DSI is expected to wrap up its investigations before then, he said.
He added his ministry would form eight panels tasked to expedite the investigation of cold cases.