Police today said they were investigating if the hack was in response to a Thai court decision that has been widely protested in neighboring Myanmar.
The December 24 ruling resulted in death sentences for two Myanmar men convicted of murdering two British backpackers.
Protesters believe the men were scapegoats and have threatened to boycott Thai goods after a trial that raised many unanswered questions about police and judicial conduct in Thailand.
Several police websites were either offline or still displayed the hackers' message today evening, hours after the online attack was staged late Monday.
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Thai police spokesman Dejnarong Suthicharnbuncha said about "two or three" websites were affected but Thai media listed more than 12.
"I received an initial report that the hackers are from another country," Dejnarong said. When asked if he meant they were from Myanmar and whether the hack was in response to the Koh Tao verdict, he said, "It's possible. We are investigating."
The men, Win Zaw Htun and Zaw Lin, were convicted of murdering David Miller, 24, and Hannah Witheridge, 23 whose bodies were found on the island of Koh Tao on September 14, 2014. Witheridge had also been raped.
Police rushed to solve the crime, under intense pressure to limit negative publicity to the tourism industry, but the investigation and trial drew widespread criticism.
Police were criticized for not properly securing the crime scene, conducting more than 200 random DNA tests, releasing names and pictures of suspects who turned out to be innocent, mishandling crucial DNA evidence from the victims and allegedly torturing their prime suspects.