TOKYO—Japan will continue to rely on nuclear power as a central part of its energy policy under a draft government plan, effectively overturning a pledge by a previous administration to phase out all nuclear plants.

Skepticism about nuclear power has been running high among people in Japan since the March 2011 accident at the Fukushima Daiichi plant, the worst nuclear disaster globally since Chernobyl. But Prime Minister Shinzo Abe has made it clear since taking office in late 2012 that he aims to restart reactors that are...