The Consultative Council for National Reconciliation made the appeal on Friday, the Korean Central News Agency reported Saturday.
"Are you ready to come out for a dialogue with the DPRK, without raising 'the north's nuclear issue?'" said the DPRK official organ in charge of dealing with inter-Korean relations.
"South Korean authorities do not hesitate to reveal their scheme for sanctions against and pressure on the DPRK, finding fault with its legitimate step for bolstering the nuclear force for self-defense," it said.
Other demands for working on national reconciliation include stopping military exercises with the United States, ending collaborations with foreign countries on inter-Korean issues, rejecting UN sanctions and releasing a dozen DPRK women allegedly kidnapped by the South Korean intelligence services, said the council.
South Korean President Moon Jae-in has said that he would start dialogue with Pyongyang if the latter stops its nuclear and missile programs.
The article was first published in the Global Times.