Barret was quoted as saying that he congratulated Croatia on the completion of its EU accession negotiations and that Ireland was looking forward to Croatia's full membership in the EU in mid-2013.
The Irish official expressed hope that the European Union would solve most of its financial problems by that time.
Ireland supports the admission of small and medium-sized countries which can accomplish their priorities and goals in the EU together, Barrett said, adding that being small did not mean that one could not give their contribution to the EU.
Bebic said that Croatia recognised the importance of small and medium-sized countries building ties in the EU.
As for Croatia's regional policy, Bebic said that Croatia found it important that its neighbouring countries strode on the same path of European integration processes and shared common values for the sake of lasting peace and political and economic stability.
Regarding the economic cooperation between Croatia and Ireland, he called on Irish business people to invest into Croatia.
"We are looking forward to the enhancement of our relations not only on the economic but also on other fronts," the Croatian official said.
He voiced hope that Ireland would be among the first countries to ratify Croatia's Treaty of Accession with the EU.
During his official visit to Dublin, Bebic will also meet Irish President Mary McAleese and tour Trinity College.