He was responding to questions from the press about the new pope's first moves and if they showed the direction of the Church.
Josipovic will attend the pontiff's inauguration on Tuesday.
Reporters also asked if the public had the right to know everything about the ministers.
"There is a private sphere, of course, but when it comes to assets and how they were acquired, we officials have the obligation to report them to the Conflict of Interest Commission, and there's also a legal provision under which we have the duty to explain what we acquired and how."
The president was also asked to comment on some claims that there was a political campaign against Dinamo football club executive director Zdravko Mamic, who was taken into custody yesterday after he made ethnic slurs against Sports Minister Zeljko Jovanovic.
"I've said yesterday how socially harmful it is to label anyone, whether a minister or not, on national grounds and insult them. That's also an insult against an entire minority in Croatia as well as against the entire Serb people. That's completely unacceptable and should be roundly condemned, especially language that can be described as verbal vandalism."
The president added that it was now up to the judiciary to say if Mamic's outburst, "apart from this harmful social dimension, has another dimension too."
He also commented on "statements positioning Croatia as a country only for Croats."
"Croatia is the country of all of its citizens and each of them must enjoy all human as well as minority rights. The Constitution guarantees that. We have to protect and respect and defend that. This makes Croatia a good country, a country where people can live well, comfortably and humanely."
Josipovic also spoke against any form of nepotism. "Every position in civil service or anywhere else must be equally available to all and this is a principle we must all defend together."