The comments by the tough-talking former army chief, Prayut Chan-O-Cha, who is also prime minister, come after Britain offered to help with the police investigation, amid deepening concerns over the handling of the probe.
Thai police have charged two migrant workers from Myanmar with the murder of David Miller, 24, and the rape and murder of Hannah Witheridge, 23, after the tourists' battered bodies were found on the southern island of Koh Tao on September 15.
But unease over the case has deepened because of reports that the suspects were tortured into confessing -- an allegation Thailand has strongly denied.
"I consider Koh Tao case to be reliable," Prayut told reporters, adding there were several pieces of evidence to charge the migrant workers.
"Anyone can come to Thailand, but don't forget that what is our issue, is our issue," he said of British offer of help.
"We managed to arrest suspects swiftly even though it seemed impossible at the beginning," he said.
The arrests followed intense scrutiny of Thai authorities, which had been accused -- in criticism led by the British media - of bungling the investigation in the days after the crime.
On Tuesday Britain's envoy in Thailand met Thai and Myanmar officials in Bangkok to discuss the investigation.
A day earlier, Thailand's top diplomat in London was summoned to hear the UK stress its "real concern" about the handling of the case, which has further dented Thailand's already battered reputation as a tourist paradise.
In a statement junior foreign minister Hugo Swire "reiterated that the UK police stood ready to assist with the investigation and subsequent legal process".
Thai police have said the two Myanmar suspects confessed to the crime and their DNA matched samples taken from Witheridge's body.
Myanmar has also raised fears over the treatment of its nationals.
"We hope Thai authorities will act with balance and accuracy to prosecute the offenders according to the law and not take action wrongly against those who didn't commit the crime," an official from the Myanmar president's office in Naypyidaw told AFP.
The grisly murders on the normally tranquil Thai island delivered a fresh blow to the kingdom's image as a tourist haven after months of political protests that ended in May's army coup.
