The international hacking group Anonymous said on its Facebook page that 14 Thai police websites had been attacked. Of those it listed, nine were inaccessible on Tuesday.
Police on Tuesday confirmed the attack on its websites but said there was no confidential data on the public websites.
"They're not good enough to hack into our system and steal any of our data," police spokesman Dechnarong Suthicharnbancha said.
In a 37-minute video posted on the Anonymous Facebook page on Sunday, a masked person questioned the competency of the Thai police force and its handling of this and other cases.
On December 24, a Thai court found Zaw Lin and Win Zaw Htun, both 22, guilty of killing Hannah Witheridge, 23, and David Miller, 24, whose battered bodies were found on a beach on the southern Thai holiday island of Koh Tao in 2014.
The investigation into the killings drew allegations of police incompetence, torture and mishandling of evidence. A judge dismissed the allegations of torture, saying there was no evidence it took place.
The verdicts sparked anger in Myanmar where hundreds held protests outside the Thai Embassy in the commercial capital of Yangon, calling for the two to be released.
The words "Failed Law", "We Want Justice", and a hashtag #BoycottThailand were displayed on some of the hacked sites, along with the name of Myanmar-based "Blink Hacker Group".
Reuters was unable to verify who carried out the attack on the police websites.
© Thomson Reuters 2016