"We are getting closer to solving this case," Deputy Prime Minister and Defence Minister Prawit Wongsuwan said yesterday, "Now, we know for sure that the culprits are Asians".
The bodies of the two Britons were found on the island's beach early Monday.
Prawit, however, declined to give any specific timeframe for the arrest of the culprits.
"We have already dispatched experts from all relevant fields to the crime scene. They are doing their best," he said.
The brutal killings of the tourists have made headlines in both local and international media. Evidence suggests that the female victim was sexually violated.
The Office of Police Forensic Science chief, Lt-General Kamrop Panyakaew, disclosed that a unit under his office's supervision had been assigned to collect DNA samples of all people on Koh Tao.
This move is in addition to the collection of DNA samples from 30 suspects earlier.
"We will submit one set of DNA samples and wait for their results before collecting another set of samples. We will do this until we find the culprits," Colonel Chaiyasak Uakrissadathikarn, the deputy chief of the local forensic science unit, said.
Provincial Police Region 8 chief Lt-General Panya Mamen has now also ordered police to trace workers on fishing trawlers who had stopped by on Koh Tao on the day of the crime, according to Chumphon police chief Maj-General Suttinat Sudyod.
Koh Tao is also near Chumphon province. According to Suttinat, police are looking for possible clues from coastal fishermen's villages and fishing trawlers' crewmen, too.
More than 50 marine policemen used speedboats to check fishing trawlers in the area yesterday.
Surat Thani Police Station superintendent Colonel Paisal Sangthep admitted that the Bt200,000 bounty had not attracted any tip-off yet.
"If you have useful information, please come forward," he said.
An informed source said police were in the process of questioning two suspects. One of them is a Thai while the other is a migrant worker.
Entrepreneurs on Koh Tao are now being asked to increase lighting and install CCTV to help boost safety on the island.