TOKYO — The Liberal Democratic Party of Prime Minister Shinzo Abe has governed Japan in one way or another for all but four of the past 61 years, a winning record that reflects the political inertia of a society that values stability and tradition.

But even by the standards of Japanese politics, Mr. Abe’s landslide victory in national elections on Sunday was stunning. For the first time, voters gave the Liberal Democrats and their allies more than two-thirds of the seats in Parliament — a supermajority that could allow Mr. Abe to realize his long-held ambition of revising the clause in the Constitution that renounces war and make Japan a military power capable of global leadership.

Opinion polls show only lackluster support for Mr. Abe’s security agenda or even his program to revitalize the Japanese economy, but the public appeared unwilling to take another chance on the opposition Democratic Party, which stumbled badly in its last, rare stint in power, most notably in its response to the 2011 earthquake and Fukushima nuclear disaster.

The vote for stability at home, though, is likely to provoke unease across Asia, where memories of Japanese militarism in World War II endure and the prospect of a more assertive Japan will add to worries over China’s territorial ambitions and North Korea’s nuclear program.