After decades of inactivity, the CMP, in the past two years, has already exhumed the remains of some 400 missing Greeks and Turks at dozens of mass graves around the island and has identified 125 of them, allowing them to be properly buried by their families.
Until recently, the fate of the missing – some 1,500 Greeks and 500 Turks – was one of Cyprus's most taboo subjects, the names of those who disappeared rarely mentioned.
"The two communities initially decided not to deal with this issue and to hide it," says Elias Georgiades, the top Greek Cypriot member of the CMP.
"Practically every family in Cyprus has a relative who is either missing or dead. This is a wound, a wound that touches all of us and that gave great suffering to those involved."
He adds: "It is logical to expect that once you solve problems like this, it will help improve the climate. The opposite is also true – if we don't deal with this wound, it will lead to further problems."
Cyprus, ruled by the Ottomans and then by the British, gained its independence in 1960. But by 1963, the new country made up of Greek and Turkish speakers was in shambles, with intercommunal violence leading to the arrival of UN peacekeepers. The island was partitioned in 1974, after Turkey invaded in the wake of a Greek-led coup that sought to reunify Cyprus with Greece. The Turkish-occupied northern part of the island in 1983 declared itself the Turkish Republic of Northern Cyprus, a ministate of 264,000 currently only recognized by Ankara.
After decades of futile negotiations, the two Cypriot communities have recently restarted talks in the hope of finding a settlement that will lead to the island's reunification.
Ahmet Erdengiz, an official with the Turkish Cypriot Foreign Ministry and a member of the CMP, says he believes the group's work could be helpful in bridging the gap between Greek and Turkish Cypriots.