Pioneer, one of several car navigation system makers battling the bug, had received several hundred phone calls since the problem started at 9 a.m., a spokeswoman said.
About 450 Pioneer workers manned telephone lines and staffed service centers over the weekend to help customers with the GPS problem, she said.
Some 95,000 car navigation units sold in Japan may be unable to cope with an internal date change in the system, the Ministry of International Trade and Industry said.
Four Japanese manufacturers of GPS systems have completed updating only about 170,000 of the estimated 260,000 units sold in Japan since 1996 and believed to be still in operation.
Japanese drivers are heavily reliant on the navigational devices because most streets in urban centers such as Tokyo are unnamed and follow curving paths laid out among a tangle of property lines.
Japan's Maritime Safety Agency has received reports that ships with older GPS systems are in or near territorial waters but has not received any distress calls as of Sunday noon, a spokesman said.
At midnight GMT, the 24 satellites of the Global Positioning System, which provide navigational data from 11,000 miles out in space, switched their timing system back to zero.
The rollover is because the system, which uses radio signals from satellites to provide navigation data, was designed to ignore calendar dates but keep precise time measured in seconds and weeks.
Only 1,024 weeks were allotted from January 6, 1980, before the system is reset to zero.
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