A Soyuz rocket carrying the Progress cargo ship lifted off on schedule at 05:58 GMT from Baikonur cosmodrome in Kazakhstan, Russian space agency Roscosmos said.
After around nine minutes, the Progress ship "separated normally" from the third stage of the Soyuz rocket and set off on a two-day trip to the ISS, Roscosmos said. It is due to dock with the orbiting station on Friday at 0834 GMT.
A Progress ship taking food and equipment to the ISS crew in December lost contact with mission control minutes after launch due to a malfunction during the separation of the third stage of the Soyuz rocket.
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The spaceship then burned up in the atmosphere over a remote area of Siberia.
A commission appointed to investigate the malfunction concluded in January that it was caused by the break-up of the third stage engine, either due to "foreign materials" getting inside or an "assembly fault".
Wednesday's launch was the last ever for a particular modification of the Soyuz rocket that has been used since 1973 and has failed 22 times out of 788 launches, Roscosmos said.
Russia is currently the only country executing manned space flights to the ISS, which are carried out using Soyuz rockets.
The next manned launch to the ISS has been postponed until April 20 from late March, Roscosmos announced this month. The reason for the delay, which is not unusual, has not been made public.
Russia's space industry had suffered a string of setbacks and launch failures in recent years, while corruption scandals have plagued its new space port in the Far East.
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