Abhisit told CNN in an interview broadcast on Friday that it was not yet clear who had approved the practice of setting minority Muslim Rohingya migrants adrift, but added that he was trying to find out.
"All the authorities say that it's not their policy but I have reason to believe that some instances of this have happened," Abhisit told CNN when asked who was behind the policy of towing them out into the open ocean.
"And if I can have the evidence as to exactly who did this I will certainly bring them to account," he said.
Hundreds of Rohingya have been rescued in Indian and Indonesian waters in recent weeks, some covered with welts.
They have said they were detained and beaten before being set adrift with few supplies by Thai security forces.
Rights groups fear scores may have perished. A photograph apparently showing the Thai army towing refugees out to sea has been published in the media and similar images were shown by CNN on Friday.
Abhisit however dismissed the Rohingya's claims that they are fleeing poverty and repression in military-ruled Myanmar, insisting that they were economic migrants who were posing a strain on Thailand.
"I believe that at times when there is... a lot of pressure in terms of the numbers of these people coming in, there are attempts to try to let these people drift to other shores," Abhisit said.
"The one thing that is clear is that when these procedures do occur it is done on the understanding that there is enough food and water supplied," he added.
Many of the migrants have told of being set adrift with minimal supplies to eat and drink.
Thailand has previously denied all allegations of cruelty but the issue has caused embarrassment for its fledgling government.
It is set to be discussed at an Association of Southeast Asian Nations summit in Thailand later this month.