SEOUL—North Korea test-fired a new type of tactical guided weapon at different targets, marking “an event of very weighty significance,” the country’s state media reported, as the Kim regime signals a firmer stance toward the U.S. following the breakdown of denuclearization talks.

Leader Kim Jong Un supervised and guided the tactical weapon’s performance from an observation post on Wednesday, deeming that its flight and warhead load “were perfectly verified,” the North’s state media said early Thursday. Pyongyang didn’t provide...