South Korea's Yonhap News Agency said Monday one report compared Kim to Adolf Hitler.
Yonhap said the Korean People's Army released coordinates of the Chosun Ilbo, JoonAng Ilbo and Dong a Ilbo newspapers and the broadcast stations, saying they are potential targets of North Korean military action.
"If the [South Korean President Lee Myung-bak] group recklessly challenges our army's eruption of resentment, it will retaliate against it with a merciless sacred war of its own style as it has already declared," the general staff said in the ultimatum reported by North Korea's Korean Central News Agency, Yonhap reported.
Yonhap said South Korea defended the country's freedom of the press and issued a statement saying it "will maintain a posture to immediately cope with any North Korean provocation."
A South Korean military official said no particular movements in the North Korean military had been observed.
The threat by the North was made in response to South Korean media coverage of a festival marking the 66th anniversary of the Korean Children's Union in Pyongyang.
Some South Korean reports said the event was a public relations ploy to boost support for the new leader. The television arm of the Dong-a Ilbo newspaper compared Kim to Adolf Hitler, Yonhap said.