TOKYO — Japan’s ruling Liberal Democratic Party kicked off a two-week campaign on Thursday to pick its next leader to succeed Prime Minister Fumio Kishida as it seeks to win back public trust eroded by a political funds scandal.

The race to choose a new party president to replace Kishida in that role means the winner will also become prime minister early next month when the Diet, Japan’s parliament, reconvenes as the LDP dominates the legislature as the majority party.