North Korea's military Tuesday issued an "ultimatum" saying it would attack without warning if anti-North Korean activities continued in the South.

The warning came after protestors in Seoul on Monday burned portraits of North Korea's founder Kim Il-Sung, his son Kim Jong-Il and grandson and current leader Kim Jong-Un.

The act coincided with national celebrations in North Korea for the 101st anniversary of the birth of Kim Il-Sung, a day it reveres as "The Day of the Sun".

"All the service personnel and people of the DPRK (North Korea) are simmering with towering resentment at this monstrous criminal act," the army's supreme command said in a release carried on the official Korean Central News Agency.

In an "ultimatum" to the South, it warned: "Our retaliatory action will start without any notice from now as such a thrice-cursed criminal act of hurting the dignity of the supreme leadership of the DPRK is being openly committed in the heart of Seoul under the patronage of the puppet authorities."

It added that the armed forces "will start immediately their just military actions to show how the service personnel and people of the DPRK value and protect the dignity of the supreme leadership.

"The military demonstration of the DPRK's revolutionary armed forces will be powerful sledge-hammer blows at all hostile forces hurting the dignity of the supreme leadership of the DPRK."

The threat came as North Korea was expected to carry out a missile launch to mark Monday's anniversary of its founder's birth.

The Korean peninsula has been in a state of heightened military tension since the North carried out its third nuclear test in February.

Incensed by fresh UN sanctions and joint South Korea-US military exercises, Pyongyang has spent weeks issuing blistering threats of missile strikes and nuclear war.

In an attempt to defuse tensions, South Korea's new president, Park Geun-Hye, in recent days has signalled the need to open a dialogue and "listen to what North Korea thinks".

But the North has rejected her proposals as a "crafty trick" to conceal Seoul's aggressive intentions.

North Korea's army supreme command Tuesday said that if South Korea really wanted dialogue and negotiations, "they should apologise for all anti-DPRK hostile acts, big and small".

The North has a habit of linking high-profile military tests with key dates, and expectations had been high of a mid-range missile test to coincide with Monday's celebrations marking the birth of Kim Il-Sung.

But unlike the centennial birth anniversary last year, there was no muscular military parade through the centre of Pyongyang and officials in Seoul said the "missile watch" could drag on for days.