In a new escalation of hostility between Washington and Pyongyang, North Korea’s foreign minister warned in a United Nations speech Saturday that a rocket attack on the U.S. mainland was “inevitable,” while U.S. warplanes flew off the east coast of North Korea in an explicit show of force.

The eight U.S. aircraft flew close to the North Korean coastline while remaining in international airspace, the Pentagon said in a statement, adding it was the farthest north of the demilitarized zone between North Korea and South Korea...