The junta has clamped down on any opposition to its overthrow of an elected government, with a crackdown on perceived slurs against the royals at the heart of its online surveillance operations.
"Lese majeste is our priority," Police Major General Phisit Pao-in, head of the Technology Crime Suppression Division, told AFP.
Twenty police officials were recently sent to reinforce Phisit's cyber patrol team of 15 civil servants, who trawl the Internet for royal insults.
Under controversial lese majeste rules, anyone convicted of insulting King Bhumibol Adulyadej, the queen, heir or regent faces up to 15 years in prison on each count.
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Phisit said his team wanted to talk to suspects to "change their attitude", while "headstrong" campaigners would face charges.
At their Bangkok offices, the owl mascot of the cyber patrol unit stands opposite a gilt-framed portrait of Bhumibol, whose picture hangs in offices and homes across the country.
For many Thais, respect for the king, patriotism and religious devotion are closely intertwined, giving him an almost divine status.
Open discussion of the succession is not possible in Thailand because of the lese majeste laws.
But the heir to the throne, Crown Prince Maha Vajiralongkorn, has yet to attain the same level of popular support as his revered father, who is the world's longest-reigning sovereign.
Some observers see the kingdom's long-running political crisis as a struggle to determine who will be in power to oversee the transition.