TOKYO—Three years after the Fukushima Daiichi nuclear accident, the stricken plant's operator estimates it is still six years away from grappling with the biggest cleanup problem: removing melted nuclear fuel.

Tuesday marks the anniversary of the March 11, 2011, earthquake and tsunami that led to meltdowns of three of the site's six reactors and explosions at reactor buildings that left them filled with concrete and metal rubble—the worst nuclear accident since Chernobyl.

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