KDDI said in a statement at 9:00 a.m. on Monday (0000 GMT) that data transmission had been broadly restored but users might experience difficulty in making voice calls due to restrictions.
The disruption, which began in the early hours of Saturday morning, was caused by equipment malfunction and affected services from weather data to parcel delivery and banking.
"The main risk is that more outages are possible because network complexity is difficult to manage," said Redex Research analyst Kirk Boodry, who publishes on the Smartkarma platform.
KDDI's shares, which were down 1.5% at 10:03 a.m., are up 26% year-to-date.
(Reporting by Sam Byford and Sam Nussey; Editing by Tom Hogue and Muralikumar Anantharaman)