SEOUL—North Korea's latest attempt to fire off a long-range rocket followed the same pattern as previous efforts except for one potentially significant difference: this time it admitted failure.

Nearly a month after announcing its intentions, North Korea early Friday launched a newly designed, three-stage rocket, which it said was destined for space but other countries feared was a intercontinental missile in disguise. Less than two minutes after launch, the rocket crashed off the west coast of South Korea, whose navy Saturday...