Thailand's strict lese-majeste law makes it a crime to defame, insult or threaten the monarchy. Those who are found guilty face up to 15 years in prison.
Udomdej called on Thais to protect the royal institution and abide by the law protecting it.
"There are people who violate this law and this worries Prime Minister Prayuth. Most people love and respect the monarchy but there are some who think differently," Udomjej told reporters, referring to his predecessor as army chief, Prayut Chan-o-cha.
"I ask for cooperation from all Thais to help protect the monarchy."
Prayut seized power in a coup on May 22 after months of protests against a government loyal to an influential ousted premier, Thaksin Shinawatra.
Under military rule, lese-majeste charges have skyrocketed and Prayut, a staunch royalist, has repeatedly vowed to root out critics of the monarchy.
Deputy Prime Minister Prawit Wongsuwan, who is also defence minister, said the government was seeking the extradition of lese-majeste suspects living abroad.
"We must bring these Thais back to face justice," he said.
Rights groups say the junta has used the laws to intimidate its critics, something the government denies.