Halilhodzic threatened to leave his press conference when asked whether his Muslim players would observe Ramadan, which began on Sunday, while he also slammed some members of the Algerian press for claiming he had advised his squad against following the traditional fasting practices.
The 61-year-old Bosnian, who is also a Muslim, was furious that journalists would ask about something so "private".
"Stop asking me about Ramadan or I will get up and leave," Halilhodzic said.
"When you ask the question, you lack respect and I'd like you to focus on the football and nothing else.
"“This is not the first time I coach a team with Muslims, I'm a Muslim myself.
"I have always allowed the players to make their own decision."
Ramadan is the ninth month of the Islamic calendar and is traditionally marked by fasting during daylight hours, including drinking water.
Reports in the Algerian media had claimed Halilhodzic had told his players to avoid fasting as they prepare for their round of 16 clash with Germany at the FIFA World Cup but the coach dismissed those rumours.
"Unfortunately, I have read some newspapers, and one in particular, who continue to tarnish my image and question my honour and integrity," he said.
"They have called for hatred and aggression against Vahid and his entourage, that's disgusting."
Some Islamic clerics have also claimed it is alright for individuals to fast at another time for special events, which has meant some Muslim athletes have avoided fasting when at the Olympics or when playing professionally.
But other athletes have claimed fasting does not affect their ability to perform at an elite level with Ivory Coast defender Kolo Toure having told the English Professional Footballers' Association last week that he has never had an issue during Ramadan.
"You definitely need discipline. For me, the first five days are difficult but after that, the body just starts to [adapt] and you feel really happy," Toure said.
While Algeria is the only predominantly Muslim country to have reached the knockout stages of the World Cup, France, Switzerland, Nigeria, Belgium and Germany also have Muslim players.
Algeria will face Germany in Porto Alegre on Monday.
