Thailand's military government has requested the extradition of several people suspected of insulting the monarchy after the death of King Bhumibol Adulyadej, the foreign minister said on Tuesday.

Sensitivities are running high in the Southeast Asian country following the death of the revered king on October 13, after seven decades on the throne.

It has also led to the rise of ultra-royalist vigilante groups who say they will punish anyone perceived to have insulted the monarchy during a highly sensitive time for Thailand.

There has been a jump in the number of prosecutions for criticism of the monarch, the regent or the heir to the throne. Known by the French term lese majeste, the crime can carry a jail term of up to 15 years for each offence.

The law has curtailed public discussion about the monarchy's role and its future following the death of King Bhumibol, who was seen as a unifying figure.

Last week, the government said it sought the prosecution of 19 lese majeste suspects in seven countries. It has not identified the individuals or the countries.

Foreign Minister Don Pramudwinai told reporters letters had been sent to the countries where the suspects live.

"There may be a problem because if these crimes aren't illegal in the other countries, it will make extradition difficult," the minister said. "However, we can still ask for cooperation."

Since taking power in 2014, the junta, known officially as the National Council for Peace and Order, has taken a tough stance on dissenters.

Thailand's government has been criticised by the international community over prison sentences for civilians found guilty of violating the lese-majeste law. No country has openly indicated readiness to extradite any suspect to Thailand.

"First, the extradition requests are part of scare tactics to curb the so-called violations, and second, to appease the powerful elite factions whose interests rely on ultra-royalism," Verapat Pariyawong, a visiting scholar at London's SOAS School of Law, told Reuters.

The government has urged citizens to report cases of lese majeste to authorities. It has also asked internet service providers to monitor and block inappropriate material.

"These laws are not meant to repress citizens but to protect the royal institution," Prime Minister Prayuth Chan-ocha told reporters.