After the talks, the Croatian head of state said that citizens of Kosovo and its institutions should be those that would decide on the status of Kosovo.
Rossin, a former US ambassador to Croatia, told reporters that President Mesic had given him several pieces of wise advice for the work of the UN Mission in Kosovo (UNMIK).
Mesic told reporters that he would like to see that his visit would contribute to better understanding in the region, which is, he added, in the interest of Croatia, too.
"An unstable Kosovo means the unstable region, but we want the region to turn towards Europe," he said.
The Croatian head of state said that citizens and institutions of Kosovo should be those that would decide on Kosovo's status, and that a solution should be sought in negotiations between Pristina and Belgrade with the assistance of the international community.
Asked by a reporter whether he supported the independence of Kosovo, Mesic said that citizens of Kosovo should give an answer to this question.
In this context he stressed that no solution should be imposed by force.
He added that his hosts in Belgrade on Wednesday agreed with him that there was no solution with use of force but it could be achieved through political agreements.
Mesic also met two Croatian police officers deployed as members of UNMIK staff in Kosovo.
Later in the day he will hold talks with Kosovo officials and representatives of the ethnic Croat minority living in a few villages in the area of Janjevo and Letnica, south of Pristina.