The dispute cropped up in February after the two countries' heads of state exchanged accusations concerning Italian and Croatian World war Two victims.
When dealing with issues concerning other countries, Zagreb must consult those countries before making final decision, Mesic said during the talks with Ranieri, who was at the helm of the Italian parliamentary delegation on a visit to Croatia.
The Italian official supported Mesic's assessment concerning the need to build good bilateral relations, He said that Croatia's admission to the European Union was supported both the Italian government and the entire parliament.
The talks also focused on the situation in the region, the statement said.
Mesic positively assessed Croatia's relations with neighbouring countries and commented on the issue of the final status of the UN-govern province of Kosovo.
The UN plan for Kosovo's final status foresees Kosovo's independence with international supervision and maximum protection of the Serb minority, but Belgrade said no to the plan because it means Kosovo's separation from Serbia.
There is no going back to the way it was, Ranieri said, adding that the international community should support democratically oriented political forces in Serbia.
Speaking about Bosnia-Herzegovina, Ranieri advocated growing support to maintaining the country's integrity, the statement from the President's Office said.