He said forensic tests will be necessary to check the Indonesian naval personnel,s DNA and evidence found on board the Thai trawler.
Gen Chakthip led a fact-finding meeting between Thai police and officials of the Indonesian consulate in Songkhla.
He said police have issued warrants to arrest 12 crew members of the Thai fishing boat for illegal entry while other charges will not be made until evidence is clear.
The bodies of the two Indonesian naval personnel killed on March 9 have yet to be found.
Thai police said the troubled fishing trawler might have illegally assumed the rights of a Thai boat, the Sor Nattaya 7, to enter Indonesian waters for fishing.
The trawler also left Thailand without going through the required immigration check.