SEOUL, South Korea — The governments of North and South Korea escalated their hostile warnings to the highest level in years on Friday, with each threatening to annihilate the other a day after the United Nations Security Council unanimously imposed tightened sanctions on the North for its nuclear test last month.

North Korea said it was nullifying all nonaggression agreements with South Korea, and one of its top generals claimed his country had nuclear-tipped intercontinental ballistic missiles ready to blast off. South Korea said that if North Korea attacked the South with a nuclear weapon, the government of the North’s leader, Kim Jong-un, would be “erased from the earth.”

It was the most vitriolic verbal back-and-forth between the two Koreas, still technically at war, since they engaged in an artillery skirmish three years ago, and it reflected the heightened tensions that followed the Security Council’s 15-to-0 vote to further penalize North Korea in response to the Feb. 12 nuclear test, its third.