A reporter from Gazeta Sporturilor attempted to hand the rod to Daum following a previous remark by the German that the newspaper was "only good for wrapping fish."
"Is this now comedy or do you want to speak about football," asked Daum, speaking in English. "When do (will) you start to become a sports journalist... or do you want to go somewhere else?
"This has nothing do to with football, you only want to create funny stories," he added.
Daum, who has coached clubs in Germany, Turkey, Austria and Belgium, has been involved in several heated exchanges with the local reporters in the past, at one pointing saying that he considered himself to be "more Romanian" than they were.
Romania, who host Armenia on Friday, are fourth in European World Cup qualifying Group E with six points from six games and have only a slim chance of reaching the playoffs for next year's tournament in Russia.
They have won two, drawn three and lost three of their eight games since the 63-year-old took over after Euro 2016.