(Reuters) - Authorities in Thailand have dug up the bodies of six suspected Rohingya migrants from Myanmar at a rubber plantation near a mountain where a mass grave was found at the weekend, the military said on Wednesday.

The discovery was made in Thailand's Songkhla province near the country's border with Malaysia around 4 km from the site where the 26 bodies were found a few days ago.

"Villagers living nearby told us the bodies buried here are the bodies of Rohingya migrants from Myanmar from nearby human trafficking camps," Colonel Jatuporn Klampasut, deputy secretary general of the Internal Security Operations Command (ISOC) Region 4, told Reuters.

The bodies were four women and two men, said Jatuporn.

Many illegal migrants in Thailand are Rohingya Muslims from western Myanmar and from Bangladesh who brave often perilous journeys by sea to escape religious and ethnic persecution.

Thousands arrive in predominantly Buddhist Thailand every year, brought by smugglers. Many are then taken into the jungle where traffickers demand a ransom to smuggle them south across the border to mainly Muslim Malaysia.

Asked by reporters whether there had been official complicity in trafficking humans, Deputy Prime Minister and Defense Minister Prawit Wongsuwan told reporters in Bangkok: "There must be. This is not acceptable."

Authorities on Tuesday said they had found a second, abandoned camp used for human trafficking. Three people were rescued from the near the camp, Thai police said.

The United States, which has censured Thailand for failing to act against human trafficking, has called for a speedy and credible inquiry into the discovery of the mass grave.

Prawit said the United States has praised Thailand for the way it had handled the recent discovery of the mass graves and suspected human trafficking camps.

"The United States has praised us that we have done this transparently," he said.

Police in Thailand have arrested four men - three Thais and a Burmese national - on suspicion of human trafficking. Arrest warrants have been issued for a further four who are on the run.

A police officer based in Padang Besar, who spoke on condition of anonymity, said that police intelligence showed there could be three more camps on the same mountain range.

"There are three camps on that mountain with up to 700 people in each camp we are told," said the officer.

"It is just a matter of time now whether we can find them as we've been told the human traffickers are being tipped off and are moving their camps."