Judge Aydin Sefa Akay was one of 41,000 people arrested in the aftermath of the failed July putsch against Turkish President Recep Tayipp Erdogan.
The UN court ordered late last month that he should be released by Wednesday so he can return to his work in The Hague.
Akay's incarceration has paralysed an appeals court, in which a former Rwandan minister is calling for a 30-year jail term imposed for his role in his country's 1994 genocide to be overturned.
The court's president has insisted that Akay, a former diplomat who was nominated to the bench by Ankara, has diplomatic immunity.
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Now lawyers for Rwandan Augustin Ngirabatware have filed a motion to the tribunal to "report the non-compliance of the government of Turkey to the United Nations Security Council".
"Because Turkey refuses to release Judge Akay, Dr Ngirabatware's case is at a standstill," defence lawyer Peter Robinson wrote in his motion.
"He remains in prison for a crime he did not commit, waiting for a hearing he cannot have."
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