The battered bodies of David Miller, 24 and Hannah Witheridge, 23, were found on the southern resort island of Koh Tao on Monday.
Distraught relatives of Witheridge broke down in tears and hugged each other ahead of a police briefing in Bangkok on Thursday, as the investigation continued to draw a blank.
Thailand's military ruler Prayut Chan-ochha on Wednesday drew condemnation after questioning the safety of female tourists in the kingdom.
"They think our country is beautiful and is safe so they can do whatever they want, they can wear bikinis and walk everywhere," Prayut -- who is also prime minister -- told government officials.
But "can they be safe in bikinis... unless they are not beautiful?"
The British embassy in Bangkok said it had contacted the Thai foreign ministry raising its "concerns" over his remarks and to ask "for clarification", according to an embassy statement.
AFP