The meeting took place in the Jordanian capital Amman on the margins of the World Economic Forum for the Middle East and a meeting of G11, which gathers average-income countries.
Karzai said that the present situation in Afghanistan was in many aspects much better than could be concluded from media reports. He particularly highlighted the progress made in the economic sector and education.
The Afghan president thanked Croatia for its contribution to the peacekeeping mission in his country, expressing satisfaction with Croatia's plan to double the number of its personnel there.
Croatia currently has 150 troops in Afghanistan.
An agreement was reached in principle for the Croatian president to visit Afghanistan and for a high-level Afghan mission to visit Croatia. The Afghan delegation would look into ways of boosting bilateral cooperation.
The two presidents also discussed the possibility of Karzai visiting Croatia.
On Friday evening, Mesic attended a formal dinner hosted by King Abdullah II in honour of the participants in the World Economic Forum.
Mesic had a brief informal meeting with Arab League Secretary-General Amr Moussa. They talked about the current situation in the Middle East and Croatia's application for non-permanent membership of the United Nations Security Council.