"The HND wants relevant bodies to act as they are obliged to act when death threats are made, and protect colleague Cicak," the HND said in a statement signed by its vice-president Zdenko Duka.
The HND recalls that the nature of the journalistic profession is reporting based on true facts, and free comments.
"If someone is dissatisfied with certain articles, they can challenge them by using democratic means, denials, comments, through the HND Council of Honour or a court, but threats are unacceptable," it is said in the statement.
Cicak, a columnist with the Jutarnji List daily, said on Sunday that he had received a death threat by mobile phone from Boris Gotovina, the brother of Croatian Army general Ante Gotovina who is awaiting trial at the Hague war crimes tribunal.
Asked if police had interviewed Boris Gotovina, Police Directorate spokesman Krunoslav Borovec declined to answer.
Cicak said he had received the threat over his column in Saturday's edition of the newspaper.
Cicak phoned in the Croatian Television show "Nedjeljom u dva" yesterday, saying Gotovina had called him on his mobile phone and threatened to kill him over the column headlined "Hero Defending Himself by Accusing Fellow Fighters".
Cicak said he reported the threat to the police and that three police officers were posted in front of his house.
The show's host, Aleksandar Stankovic, expected that Boris Gotovina would also phone in, but that did not happen.