The comments from Ri Yong Ho, the North Korean military's chief of general staff, came as the country marked the 80th anniversary of the founding of its army, Voice of America reported.
Ri said the country had "powerful, modern weapons" that could defeat the United States in a single blow but did not elaborate on the weapons.
White House spokesman Jay Carney urged the North to avoid hostile or provocative acts, saying they would do nothing to advance peace on the Korean peninsula or in northeast Asia.
In a televised speech from Pyongyang's House of Culture, Ri said the North would not tolerate violation of its territory by South Korea or the United States, Yonhap reported.
Kim Jong Un, North Korea's leader, was in the audience but did not speak.
Ri also again threatened a "sacred war" over what it called South Korean President Lee Myung-bak's insulting the North's Kim.
Lee has urged Kim to abandon the collective farm system and devote more attention to human rights and defector issues.
The South Korean president also said the North had wasted about $850 million on its failed rocket launch April 13 and said the country could have spent that money for food for its 24 million people.