TOKYO—Japan's tsunami-stricken nuclear-power complex came closer to a catastrophic meltdown than previously indicated by its operator—who on Wednesday described how one reactor's molten nuclear core likely burned through its primary containment chamber and then ate as far as three-quarters of the way through the concrete in a secondary vessel.

The assessment—offered by Japan's government and Tokyo Electric Power Co., the operator of the Fukushima Daiichi nuclear complex—marked Japan's most sobering reckoning to date of the...