The two dignitaries were speaking to the press after a regular meeting of the Croatian and Bosnian Bishops' Conferences in Sarajevo.
Cardinal Puljic reiterated his disagreement with any changes which legalised the existing state in Bosnia and Herzegovina, which he described as unjust, including consequences of ethnic cleansing.
He said the injustice stemmed from the existence of two entities (Serb, Croat-Muslim) because the Croats were not equal in either in the adoption of laws.
Cardinal Puljic wondered why the international community was "washing its hands" of the Dayton peace agreement it had created and was ostensibly letting Bosnian politicians make decisions.
"The international community cannot not be responsible," he said, adding that Dayton II was the only logical step forward to eliminate the existing injustices, which he said were also reflected in the fact that the current number of Catholics in Bosnia was half the prewar number. He added this was why Bosnian bishops were so outspoken as to what kind of constitutional changes they wanted.
In Bosnia's new constitution, the Croats must be able to recognise their identity, rights and freedoms, said Cardinal Puljic.
Cardinal Bozanic said the constitution of every country was an important document on which bishops had the right and the duty to voice their opinion, including when it referred to Bosnia and Herzegovina.
The Zagreb Archbishop said Croatia's bishops supported their Bosnian colleagues' position on this matter because they were best acquainted with the position on the ground.