North Korea has demanded an apology from South Korea for a protest in Seoul, where effigies of Kim Il-sung and his son and successor, late leader Kim Jong-il, were burned.
A day after festivities to mark the 101st birthday of its first leader, North Korea issued new warnings against the US and South Korea.
The two countries are watching closely for signs of whether North Korea will conduct a medium-range missile test in defiance of international concerns.
State media said the Supreme Command of the Korean People's Army issued an ultimatum demanding an apology from South Korea for "hostile acts" and threatening that unspecified retaliatory actions would happen at any time.
North Korea said it would refuse any offers of talks with the South until it apologised for the "monstrous criminal act".
South Korea's Defence Ministry said it had received no such ultimatum officially, noting that there is no communications line between the two countries.
North Korea launched a rocket ahead of the last anniversary of Kim Il-sung's birth, which was the centennial, but the holiday this year has been much more low-key.
Pyongyang residents gathered in performance halls and squares and took advantage of subsidised treats, such as shaved ice and peanuts.
The calm in Pyongyang has been a striking contrast to the steady flow of retaliatory threats North Korea has issued over ongoing military exercises between South Korea and the US.