Abhisit also plans to discuss co-operation over trade and fishing, and seek Indonesia's support to "create understanding" about Thailand's anti-insurgency efforts in the Muslim-majority southern provinces.
Thailand has come under international condemnation following allegations that its security forces tortured and abused Rohingya migrants, including forcing them back to sea in engineless boats.
Rights group have accused the Thai armed forces of systematic abuse of the migrants, saying that hundreds may have died after being set adrift.
|Thailand is under pressure to address claims its authorities abused Rohingya migrants [AFP]
Last week Abhisit, in an interview with CNN, admitted that some of the Rohingya might have been towed out to sea after being intercepted by Thai authorities.
Photographs apparently showing the Thai army towing refugees in boats and lining Rohingya men up on a beach have appeared in the international media this year.
In recent weeks several boatloads of Rohingya migrants were found drifting off India's Andaman islands and the coast of Aceh province in Indonesia's western island of Sumatera.
Indonesia earlier this month said that it would consider granting refugee status to hundreds of them and urged other countries to stop abusing them.
The UNHCR, the UN's refugee agency, says that at least 230,000 Rohingya are now leading a stateless existence in Bangladesh alone, having fled alleged persecution by Myanmar authorities.