The Kurir tabloid on Monday reported that Dulic-Markovic's father had hidden for two years after World War II "Ustasha criminal Ivan Jovanovic Crni, who had been sentenced to death for crimes against Serbs".
"The latest attack on the Serbian Deputy Prime Minister is unprecedented in the recent history of dishonourable behaviour of a part of the press in the empoverished and suffering Serbia," the Independent Journalists Association of Serbia said in a statement.
The Association urged Culture and Information Minister Dragan Kojadinovic to take concrete steps against papers and reporters spreading intolerance and hatred.
The Association of Radio and Television Reporters and the Association of Professional Broadcasters warned that the language of hatred in the Serbian press was turning into a hunt after political opponents and cited the case of the Serbian deputy prime minister.
"The publishing of false, incomplete and distorted information contributes to a campaign of persecution and takes Serbia to where it used to be not long ago," the associations said.
Dulic Markovic is the only Croat in the Serbian government and a vice-president of the G17 Plus party. The Serbian Radical Party has lately levelled accusations against her over her ethnic background.