The decision "lays a solid foundation for resumption of negotiations for a fair and viable comprehensive settlement of the long-standing Cyprus problem," they said in a joint declaration Tuesday.
Turkey aspires to a closer relationship with the European Union, though its relationship with Cyprus, its political adversary, has presented a roadblock.
Cyprus has been divided into a Republic of Cyprus and the Turkish-occupied north since 1974. Turkey doesn't recognize the Republic of Cyprus, a member of the European Union.
A statement published Tuesday by the Wall Street Journal said Greek Cypriot President Nicos Anastasiades and his Turkish counterpart Dervis Eroglu viewed that status quo as "unacceptable."
"The European Commission is keen to play its part in supporting the negotiations, conducted under U.N. auspices and to offer all the support the parties and the U.N. find most useful," the joint statement read.
Swim Week Miami Beach 2014 [PHOTOS]