Now, the leftist government of Prime Minister Alexis Tsipras has announced plans to make sharia optional for such disputes, following recurring criticism by rights groups and a looming ruling by the European court of human rights.
Tsipras last week said his administration would pass legislation to allow litigants to opt for a Greek court to resolve family disputes, instead of appealing to Islamic jurists known as muftis.
For family law matters, Greek Muslims generally seek recourse to muftis for things like divorce, child custody and inheritance. Rights groups say it is a system that frequently discriminates against women.
"Over the next few days we will table an amendment in parliament... making the mufti's jurisdiction optional," Tsipras said from Thrace, the poor, mostly rural northeastern region bordering Turkey, where the 110,000-strong Muslim minority mainly resides.
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The issue has its origins in the period after World War I, and treaties between Greece and Turkey that followed the collapse of the Ottoman Empire.
The 1920 Treaty of Sevres and the 1923 Treaty of Lausanne stipulated that Islamic customs and Islamic religious law would apply to thousands of Muslims who suddenly became Greek citizens.
The move comes as the European Court of Human Rights (ECHR) is examining a complaint brought against Greece by a 67-year-old widow, Hatijah Molla Salli, who is locked in a heritage dispute with her late husband's sisters.
When Salli appealed to Greek secular justice, she initially won her case. But the Greek supreme court in 2013 ruled that only a mufti had the power to resolve Muslim heritage rights.
The ECHR is to discuss the case on December 6, and Salli's lawyer Yannis Ktistakis says Tsipras' timing is no coincidence.
He added that what Greece should do is completely eliminate the rule of sharia law on its territory, noting the patriarchal nature of Greece's Muslim community.
"The compulsory application of sharia is a clear violation of the minority's rights to self-determination," the Hellenic human rights league said in a statement.
It added that Greece's "sad privilege of being the sole (EU) country still employing religious law" was constantly leading to criticism from global rights organisations
Tsipras said that under the amendment, which has not yet been tabled, litigants can still voluntarily agree to bring their dispute before a mufti for judgment.
The issue is complicated by still-terse relations between traditional rivals Greece and Turkey.
Ankara takes a close interest in the Muslim community -- which it sees as Turkish, although it also includes Pomaks and Roma -- and frequently complains to Athens on its behalf.
In turn, Greece rejects this as interference in its domestic affairs. Greek nationalists have also long regarded the Muslim minority as overtly susceptible to Turkish influence.
Another source of tension is Turkey's insistence that muftis be elected by the community, instead of appointed by the Greek state.
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