The statement appeared to leave open the possibility of some kind of talks.
"Genuine dialogue is possible only at the phase where the DPRK has acquired nuclear deterrent enough to defuse the U.S. threat of nuclear war unless the U.S. rolls back its hostile policy and nuclear threat and blackmail against the former," it said, using the shortened version of North Korea's official name, the Democratic People's Republic of Korea.
But Daniel Pinkston, senior analyst covering Northeast Asia for the International Crisis Group , said that the terms North Korea had set out were nonstarters.
Pyongyang is saying it is willing to talk only if the rest of the world acquiesces to the status quo of a nuclear-armed North Korea, a situation unacceptable to the United States and the United Nations, he said.
Meanwhile, the North Korean government continued Wednesday to prevent South Koreans from entering the Kaesong Industrial Complex, the shared manufacturing zone that sits on the North's side of the border but houses operations of more than 120 South Korean companies.
The North has also pulled out its workers from the complex, who number more than 50,000.
There had been hopes in South Korea that the North might return the situation to normal this week following the major public holiday Monday that marked the 101st anniversary of Kim Il Sung, the founder of North Korea.
But so far, Pyongyang hasn't budged. At the weekend, it dismissed Seoul's proposal of talks over the complex, saying that what happens next depended on the South Korean government's "attitude."