The Centre for LGBT Equality issued a statement on Sunday urging the police to press charges against the attackers on Saturday's Gay Pride parade in the southern coastal city of Split for hate crime.
The statement quoted a police spokeswoman as saying that the police were considering whether to press criminal or misdemeanour charges against the rioters.
The Penal Code currently in force in Croatia recognises hate crime in Article 174 on racial and other discrimination and in Article 331 on violent behaviour, the Centre for LGBT Equality said.
The motive for violent behaviour on Saturday was "hatred towards LGBT (lesbian, gay, bisexual and transgender) persons, who were constantly and deliberately targeted with hate speech," the statement said, adding that this provided grounds for pressing charges for hate crime.
"Violence and hatred must be adequately punished, and the laws of Croatia must be respected and enforced. Bringing criminal charges would guarantee an end to violence as a method of 'challenging opinions'," the Centre for LGBT Equality said.