A Soyuz-U rocket blasted off flawlessly from Russia-leased Baikonur launch pad in Kazakhstan, placing the Progress M-28M ship into a designated orbit, safely en route to the station.
On Sunday, it's set to dock at the station currently manned by Russians Gennady Padalka and Mikhail Kornienko and NASA's Scott Kelly.
The ship is carrying 2.4 metric tons of fuel, oxygen, water, food and other supplies for the crew, the Russian space agency Roscosmos said.
Despite the failures, NASA said the station is well-stocked, with enough supplies for the crew to last at least until October.
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However, the trouble-free launch today was essential for the station program, which has exclusively relied on Russian spacecraft for ferrying crews after the grounding of the US shuttle fleet.
SpaceX still hopes to meet the target of launching astronauts from US soil again aboard the Falcon-Dragon combination in December 2017, which would allow NASA to stop buying seats from Russia to get astronauts to the space lab.
Russian space officials eventually have traced the failure to a leak from fuel and oxidizer tanks in the booster's third stage, which they said was caused by a yet unspecified flaw in the interface between the cargo ship and the latest Soyuz modification, called Soyuz 2.
The Soyuz-U rocket used today is an older sub-type of the rocket, which has been the workhorse of Soviet and Russian space programs for nearly half-a-century.