Kim Yo-jong, the sister of North Korean leader Kim Jong-un / Yonhap

North Korea remained unresponsive to South Korea's calls via liaison and military hotlines Monday despite cautious optimism created after the sister of North Korean leader Kim Jong-un said the two Koreas could discuss improvements in long-strained relations.

"North Korea did not answer our opening call through the South-North joint liaison office at 9 a.m.," a unification ministry official said. A military official also said a call via the military hotline went unanswered.

The North also did not respond to the South's daily call at 5 p.m. via the liaison office.

Kim Yo-jong, the powerful sister of the North Korean leader, issued two statements last week in which she said the two Koreas could discuss improvement in inter-Korean relations, reestablishment of the Kaesong liaison office and even a summit on conditions that Seoul drops its double-standard and hostile attitudes against it.

The statements followed President Moon Jae-in's offer for a formal end to the 1950-53 Korean War in his U.N. speech. The unification ministry saw Kim's statements as positive and expressed hope for the resumption of cross-border communication and dialogue.

"It is more important than anything else to have communication in a smooth and stable manner so as to realize denuclearization, the establishment of lasting peace on the Korean Peninsula, and the advancement of relations between the South and the North through dialogue and cooperation," Lee Jong-joo, the ministry's spokesperson, told a regular press briefing.

"The government expects a swift restoration of the liaison communication line and resumption of government-to-government dialogue, as well as discussions and the creation of solutions to a variety of pending issues facing the two Koreas," she added.

Inter-Korean relations have remained in a deadlock since the no-deal summit between the United States and North Korea in early 2019. The ties chilled further after North Korea blew up the Kaesong liaison office and cut off all cross-border communication lines in protest of anti-Pyongyang leaflets sent from the South.

The lines went briefly back online in late July, but the North has not answered Seoul's regular calls ― twice a day ― again as it bristled at joint military drills by South Korea and the U.S.

The two Koreas are still technically at war, as the Korean War ended in a cease-fire, not a peace treaty. (Yonhap)