The South Korean statement refers to a set of phone- and fax-like communication channels between the rivals, which have been largely dormant for more than a year.
The comments by Kim Yo Jong followed a similar statement she issued Friday that the North was willing to resume talks with the South if certain conditions were met.
Kim Yo Jong says an end-of-the war declaration can be adopted when the Koreas lift hostile policies and unfair double standards and biased views toward each other.
Kim Yo Jong's statement came after South Korean media reported the allied militaries will begin four days of preliminary training on Tuesday before holding computer-simulated drills.
Regular drills between Seoul and Washington have been a long-running source of animosities on the Korean Peninsula, with North Korea calling them an invasion rehearsal.
The Biden administration has promised a practical, calibrated approach, including diplomatic efforts, to persuade the impoverished North to give up its banned nuclear weapons.