North Korea will take action after action to punish South Korea over anti-Pyongyang propaganda leaflets, the country's main newspaper said Monday, after the sister of leader Kim Jong-un warned of military action against the South.

North Korea has criticized South Korea almost daily in recent weeks, denouncing the sending of leaflets into the communist state as a hostile act that violates a series of peace agreements. Last week, the North vowed to cut off all inter-Korean communication lines in the first in a series of steps it will take against South Korea.

On Saturday, Kim Yo-jong, the powerful sister of leader Kim, ratcheted up tensions further by threatening that it is high time to break with South Korea, and she gave instructions for the army to take necessary measures to punish the South.

"Relentless retaliatory acts will continue," the Rodong Sinmun, the organ of the North's ruling party, said. "Our invincible revolutionary powerful military will launch an act that will take revenge for our people who have become angrier than ever."

"It is the clear willingness of our people and soldiers that no one should be tolerated for hurting the dignity of our supreme leadership," it added. "Retaliatory plans built on such a strong anger have solidly turned into our national consensus."

The paper lambasted South Korea for making little efforts to stop the sending of anti-Pyongyang leaflets by activists despite its agreement to prevent such activity, blaming Seoul for causing "worst-ever" tensions on the Korean Peninsula.

South Korean President Moon Jae-in and North Korean leader Kim Jong-un held a summit in April 2018 and agreed to stop all kinds of hostile activity, including the sending of propaganda leaflets across the border.

"The veiled hostile policy and inability of the South Korean authorities have resulted in the complete breakdown of inter-Korean relations and generated worst-ever tensions," it said. "It is pathetic that the South Korean authorities have had no intention to clean up rubbish that gives out only disgusting odor, nor has it any ability."

The paper lashed out at the South as the two Koreas marked the 20th anniversary of the June 15 Declaration adopted after the first-ever inter-Korean summit between then President Kim Dae-jung and then North Korean leader Kim Jong-il in Pyongyang in 2000.

North Korean media outlets, including the Rodong Sinmun, however, have made no mention of the summit so far amid heightened cross-border tension. (Yonhap)