TOKYO — Shigeru Ishiba, the new leader of Japan’s ruling Liberal Democratic Party, was elected the country’s 102nd prime minister on Tuesday and vowed his administration would work to win back public trust dented by a political funds scandal, revitalize the economy and bolster defenses to deal with national security threats.

Ishiba’s victory over opposition party leaders in the legislature, the Diet, was ensured as the LDP and its coalition partner, Komeito, had more than enough votes in both the upper and lower houses, and comes after he was elected president of the LDP last week.