"The Progress M-27M spacecraft ceased to exist at 05:04 Moscow time (0204 GMT) on 8 May 2015. It entered the atmosphere... Over the central part of the Pacific Ocean," Roscosmos said in a statement.
Almost all similarly-sized spacecraft disintegrate in the atmosphere or land in the oceans, which cover most of the Earth's surface.
The spacecraft, a Soviet design generally known for its reliability, blasted off for the International Space Station on April 28 carrying oxygen, water, spare parts and other supplies for the orbiting space laboratory, which has a crew of six international astronauts.
A special commission is looking into the incident, the deputy head of Roscosmos has said.
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Sources in the space industry told Russian news agencies that the accident was caused by a problem with the Soyuz rocket carrying the cargo ship into orbit, rather than the supply vessel itself.
Russia has recently suffered a series of glitches exposing shortcomings in its space programme.
A Progress supply ship crashed in Siberia shortly after launch in 2011. Moscow has also lost several lucrative commercial satellites.