TOKYO—The Japanese government is likely to decide to eliminate all nuclear power over the next two decades in a new long-term energy plan that comes amid strong public opposition to atomic energy and ahead of national elections expected in the next few months, said government officials familiar with policy discussions.

Following the Fukushima Daiichi nuclear-plant accident in March 2011, Prime Minister Yoshihiko Noda set up a council to recommend a long-term energy strategy based on three scenarios: phasing out nuclear power...