Does Japan have a president?
No. The head of state is the Emperor, and the elected chief executive is the Prime Minister.
The Prime Minister of Japan is the usual English-language term used for the head of government of Japan, although the literal translation of the Japanese name for the office is Prime Minister of the Cabinet. The Prime Minister is appointed by the Emperor of Japan after being designated by the Diet from among its members, and must enjoy the confidence of the House of Representatives to remain in office. The Prime Minister is the head of the Cabinet and appoints and dismisses the Ministers of State.
Recent Prime Ministers of Japan are:
-- beginning September 2006: Shinzo Abe.
-- beginning September 2007: Yasuo Fukuda.
On September 1 2008, Fukado resigned abruptly in an attempt to break a governmental deadlock between his party and the Diet (governing body of Japan). The Liberal Democratic Party held an internal election to nominate a replacement until a new general election could be held.
-- from September 2008 to September 2009: Taro Aso
-- from September 2009 to June 2010, Yukio Hatoyama
-- beginning June 2010, Naoto Kan