The murder of two young British tourists on Koh Tao Island yesterday was unacceptable, Thai Prime Minister Gen Prayuth Chan-ocha said.

It was unacceptable for the Thai people and the government and the local people also could not accept what had happened, he said when questioned by reporters after the weekly Cabinet meeting Tuesday.

The locals had worn black attire to protest the killings.

He said the case was under investigation, and the resort island which was popular with tourists had been sealed off as soldiers and police had been instructed to hunt down the killer or killers.

It had been reported that three migrant workers from Myanmar had been detained in connection with the incident which the police have estimated happened between 3am and 5am on Monday.

The nude bodies of the British tourists, identified as Hannah Witheridge and David Miller, both 24, were found on Monday around 6.30am.

When asked about the government action on migrant workers who had been involved in a number of criminal cases, including high profile ones, the prime minister said the government had set the registration for illegal migrant workers which was part of the solution to the problem.

He said the companies which hired illegal migrant workers would also face legal action.

There are about 1.025 million undocumented migrant workers, and 63,620 family members had registered between June 26 and Sept 13 via the One-Stop Service across the country, according to the Foreign Workers' Administration.