Stephen Dacus, head of the chain’s parent company, aims to export its success in Japan, with signature offerings like fresh prepared food.

© Kentaro Takahashi for The New York Times

The embattled leader is trying to head off a deep split in his party over a right-wing political surge, a weakened economy and turbulent trade relations with the United States.

© Yuichi Yamazaki/Agence France-Presse — Getty Images