Thanking Mesic for the decoration, Moisiu said he considered the decoration a great honour for him, his country and its people.
The Albanian president arrived in Zagreb on Saturday to attend a summit on energy, scheduled to start on Sunday.
This is probably Moisiu's last visit to Croatia in his capacity as president since his term expires in July.
The two presidents agreed that Croatia and Albania aspired to make Southeast Europe a region of peace, security and stability, and shared the goal of joining the European Union and NATO.