The rocket was launched at 1:34 p.m. local time (4:34 GMT), which was broadcast live by the country's space agency.
The rocket is expected to bring IGS-Optical 6 satellite, manufactured by Mitsubishi Electric, into the orbit, as part of the national Information Gathering Satellite (IGS) program.
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The satellite will be able to record the surface of the Earth in daylight.
Japan is spending about $500 million a year on the development and production of reconnaissance satellites, partly out of concern over North Korea's missile tests.