BANGKOK — Two workers from Myanmar confessed on Thursday that they killed two British tourists whose battered bodies were found last month on a beach in southern Thailand, police said.

The announcement followed weeks of pressure on police to solve a case that has threatened to damage the country’s important tourism industry.

Police Maj. Gen. Kiattipong Khawsamang said three Myanmar workers were detained and questioned by police, and two had admitted murdering Hannah Witheridge, 23, and David Miller, 24.

He said the other worker denied involvement in the attack on the island of Koh Tao, renowned for quiet beaches and popular diving sites.

“We are interrogating them. So far, accounts from the two men matched and they confessed they killed the tourists,” Kiattipong said by telephone.

The attack dealt a blow to Thailand’s tourist industry, which has been struggling to recover since the army overthrew an elected government and seized power in May. Martial law remains in effect.

The bodies of the two tourists were discovered on Sept. 15 in a rocky alcove along the shore close to the hotel where both were staying.

Autopsies showed that Witheridge died from head wounds while Miller suffered severe blows to the head and drowned in the surf.

Another police officer overseeing the case, Lt. Gen. Jaktip Chaijinda, said police will wait for the results of DNA tests from the suspects to see if they match samples taken from Witheridge’s body.

“We will wait until the results of the DNA tests come in before making an arrest,” Jaktip said.

Two of the Myanmar workers were detained on the island and the other in mainland Surat Thani province, police said.

Thai police have searched for clues and collected DNA samples from more than 100 men on the island in the Gulf of Thailand.

Koh Tao, which is about 250 miles (410 kilometers) south of Bangkok, is a quiet, small island a short boat ride from Koh Samui and Koh Phangan.

The latter is known for raucous “full moon” parties that attract young foreigners and Thais.