On the poster, Italians are called on in offensive words to forget Dalmatia, return Trieste and pay damages for World War Two.
Curic said a car with a swastika on its licence plate was drawn on the poster.
The poster was noticed at 0615 hours, so police believe it was put on the building in downtown Split, which also houses the British and German consulates, during the night.
Police removed the poster and are looking for the perpetrators.
Asked for a comment, the Italian Consulate referred the press to the Italian Foreign Ministry in Rome.
Croatia's Slobodna Dalmacija daily yesterday ran an interview with Fini quoting him as saying in the headline that Dalmatia, Rijeka and Istria have always been Italian territory.