The comments came as North Korea marked the 105th anniversary of the birth of its founding present, Kim Il-sung.
A huge parade in Pyongyang was held amid speculation current leader Kim Jong-un could order a new nuclear test.
Among the hardware on display appeared to be new intercontinental and submarine-launched ballistic missiles.
The show of strength comes amid mounting tension, with a US aircraft carrier group steaming towards the region.
"We're prepared to respond to an all-out war with an all-out war," said Choe Ryong-hae, believed to be the country's second most powerful official.
"We are ready to hit back with nuclear attacks of our own style against any nuclear attacks," he said.
Rows of military bands and goose-stepping and sword-wielding soldiers marched through Pyongyang's main Kim Il-sung square for the "Day of the Sun" celebrations, as a black-suited Kim Jong-un watched on.
He saluted an honour guard and took his place on the podium. At times he appeared relaxed and laughed with aides.
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