David Miller, 24, and Hannah Witheridge, 23, were found dead early yesterday with head wounds near a beachside bungalow on the island, a diving hot-spot near Koh Phangan in the Gulf of Thailand.
An island-wide search for suspects was under way with police deployed at Koh Tao's main pier.
"There are three possible suspects," southern regional police commander Panya Maman told AFP, without confirming their nationalities.
"We have set up a coordination centre which is responsible for the investigation and mobilised both Koh Tao and Koh Phangan residents to help police," Panya said.
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The bodies of the victims are due to arrive in Bangkok later today for forensic tests, said local police official Jakkrapan Kaewkhao.
The Britons, who arrived in Thailand on August 25, had been seen partying at a local bar just hours before their deaths, according to police.
Their bodies were found yesterday with a bloodied hoe discovered 35 metres (yards) from the murder scene, Jakkrapan told AFP.
The murders are likely to heap more misery on Thailand's lucrative tourism industry, which has been battered in recent months after a prolonged political crisis ended in a coup.
The army swiftly blanketed the country with a curfew and strict martial law, frightening off visitors.
Although the curfew was soon lifted from key tourist hotspots, visitor numbers have yet to rebound and martial law remains in place.
There were 389 deaths of British nationals in Thailand in the year to March 2013 - about one for every 2,400 British visitors or residents - although that figure includes natural causes.