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.
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"Since the coup, we were asked to intensify our surveillance and to focus on threats to national security," said Phisit.
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.
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.
The military takeover comes as the kingdom quietly braces for the eventual end of the 86-year-old monarch's more than six-decade reign.
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.
Since the coup, Thailand has blocked access to more than 200 Internet pages deemed a "threat to national security", including the website of Britain's Daily Mail newspaper after it posted a video about the crown prince.
"The monarchy is above any conflict," said junta spokesman Winthai Suvaree, relaying army chief Prayut Chan-O-Cha's message to foreign diplomats in Bangkok last week.
Laws are needed to protect the royals "because the monarchy cannot answer questions like normal people", Winthai added.
The coup makers have set out to purge Thai politics of the dominance of fugitive former premier Thaksin Shinawatra.
The populist politician, who was seen by his opponents as a threat to the monarchy, was ousted by royalist generals eight years ago and lives in Dubai to avoid a jail term for corruption.
But some of his supporters were seen at recent rallies wearing T-shirts proclaiming their love for the crown prince.
Parties led by or aligned to Thaksin have won every election since 2001, and a desire among the royalist elite to erase his influence as the succession looms is seen by analysts as pivotal to understanding the crisis.
Before the coup, calls for reform of the lese majeste laws had grown following several high-profile convictions. Academics urging greater debate are among hundreds of people summoned by the junta and temporarily detained in secret locations.
In 2012, the death of 61-year-old prisoner Ampon Tangnoppakul, a few months after he was sentenced to 20 years for sending four text messages deemed insulting to the royals, drew international attention to the severity of the law.
Critics have long said the royal insult legislation has been politicised, noting that many of those charged are linked to "Red Shirt" Thaksin supporters.
Under the junta, the risks are even graver as lese majeste suspects will be tried in military courts with no recourse to appeal.
"It appears to reflect a conviction among hardline elements behind the coup that Thais perceived as enemies of the monarchy must be crushed," said Michael Montesano, a research fellow at the Institute of Southeast Asian Studies in Singapore.
The wife and son of another lese majeste prisoner, Somyot Prueksakasemsuk a magazine editor and Red Shirt supporter jailed in January 2013 for 11 years were arrested and their computers seized following the coup, according to rights activists.
And earlier this month two men were jailed for lese majeste, including a host on a Red Shirt radio station, according to local media.
Phisit's cyber patrols are not alone in their efforts to wipe out any criticism of the monarchy about 20 ultra-royalist groups are helping to monitor the Internet.
They include "The Garbage Collection Organisation", led by a director of a Bangkok hospital whose goal is to hunt down offenders viewed as "trash".