It will take at least two weeks for the Supreme Court to decide whether to accept the appeal against the death sentences handed down to two Myanmar nationals convicted of the September 2014 murders of two British backpackers on Koh Tao.
Amporn Sungthong, a lawyer for the two Myanmar men, yesterday said the judges had to review the appeal request first.
She was speaking after submitting 319 pages of documents on Monday to the court appealing against an Appeal Court ruling on March 1.
She said it could take at least a fortnight before the court makes a decision.
Zaw Lin and Win Zaw Htun, both 22, were also convicted for the theft of an iPhone from one of the victims. The mobile phone, discarded near a hotel on the island, was later found by police and used as evidence.
Ms Amporn said the theft charge cannot be appealed.
If the court does not accept the appeal, it is expected the pair may cite new reasons and request another counter-appeal to have the ruling reconsidered, she said.
Zaw Lin and Win Zaw Htun were sentenced to death in December 2015 for the rape and murder of Hannah Witheridge, 23, and the murder of David Miller, 24, on the resort island on Sept 15, 2014.
In March, the Appeal Court for Region 8 upheld the death sentences.
The main arguments in the defence's appeal are that the investigation did not follow "international standards of forensic science", and that the pair were not provided legal representation during questioning.
The defence will argue against the reliability of forensic evidence and the legality of the investigation process in their appeal.
Nakhon Chompuchat, head of the defence team, said its lawyers will argue that the forensic procedures and autopsy results which confirmed DNA from the two men matched samples collected from Witheridge's body were unreliable.
According to the Appeal Court ruling, the results were in line with international standards and the pair committed the crime "without a doubt", but the defence lawyers would point out some doubt still remained and the tests may not be completely reliable, he said.