The second-stage engine "terminated prematurely" after the rocket blasted off at 10:51 am (0151 GMT) from the Tanegashima space centre in southern Japan, according to the Japan Aerospace Exploration Agency (JAXA).
It could not release into orbit the sixth satellite to the seven-unit "Michibiki" system, "resulting in a launch failure", the space agency said.
The agency has begun an investigation into what caused the problem, it said.
The Japanese geolocation system is designed to offer improved data for the country, enabling better consumer services such as car navigation systems and smartphone maps, according to JAXA.
However, the space agency announced around 40 minutes after the rocket's launch that its second-stage engine -- which ignites after the first stage of the rocket detaches -- had stopped earlier than expected.
It came after technical glitches had twice delayed the original launch.
Officially called "Quasi-Zenith Satellite System", the Japanese geolocation system is designed to work alongside others operated by foreign countries, such as the US-developed Global Positioning System.
The system will also offer crucial location-specific information services such as evacuation orders during tsunami warnings or heavy rain, the government says.
The seventh orbiter is scheduled to be launched on February 1.
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