North Korea has threatened to bolster its military presence at now-closed inter-Korean project sites and rebuild guard posts in the Demilitarized Zone, a day after it blew up its liaison office with Seoul, sharply raising tension on the peninsula.

In a series of denunciations of Seoul, it rejected an offer it said had come from the south's President Moon Jae-in to send an envoy for talks.

North Korean leader Kim Jong Un's powerful sister Kim Yo Jong called it a "tactless and sinister proposal", the official KCNA news agency reported.

The north's military also said it would resume military exercises in the border area and prepare to send leaflets to the south.

The demolition of the liaison office in the Kaesong Industrial Zone, just across the border in northern territory, came after Pyongyang vehemently condemned Seoul over anti-Pyongyang leaflets sent by defectors into the north.

Yonhap news agency has reported that South Korean Unification Minister Kim Yeon-chul, who oversees engagement with North Korea, has offered to step down, saying he takes responsibility for a worsening in relations.

Relations between the neighbours have been at a standstill since the collapse of a summit last year between the nuclear-armed north and the US in Vietnam over sanctions relief and what Pyongyang would be willing to give up in return.

Analysts say the north may now be seeking to manufacture a crisis to increase pressure on the south to extract concessions.

A spokesman for the north's military said it would deploy regiment-level units to the Mount Kumgang tourist area and the Kaesong complex.

The two zones are sites of long-closed joint inter-Korean projects: Southern tourists visited the scenic Mount Kumgang until a North Korean soldier in 2008 shot dead a woman who strayed off the path.

At the Kaesong complex, where the liaison office stood until yesterday, South Korean companies employed North Korean workers, paying Pyongyang for their labour in a lucrative arrangement for the authorities.

The north's military spokesman also said guard posts that had been withdrawn from the Demilitarized Zone under a 2018 inter-Korean agreement would be reestablished to "strengthen the guard over the front line".

Artillery units, including those in naval areas, would resume "all kinds of regular military exercises".

In an unsigned KCNA commentary, the north warned the demolition of the liaison office would prove a first step towards a "total catastrophe" in inter-Korean relations if Seoul did not "control their tongues".

Since early June, North Korea has issued a series of vitriolic condemnations of the south over the leaflets, which defectors regularly send, usually attached to balloons or floated in bottles.

Kim Jong Un's sister Kim Yo Jong

The flyers criticise North Korean leader Kim Jong Un for human rights abuses and his nuclear ambitions.

In a separate KCNA report, Pyongyang claimed that Mr Moon had on Monday offered to send his spy chief Suh Hoon and national security advisor Chung Eui-yong as special envoys.

But Kim Yo Jong said the north "flatly" rejected the offer, KCNA reported.

The two Koreas remain technically at war after hostilities in the Korean War ended with an armistice in 1953 but not a peace treaty.