Docking five minutes ahead of schedule at 03:40 GMT on Sunday, the spokeswoman told journalists: "Everything is fine, even excellent, I would say."
Progress is now the only surviving link to the station after all three American shuttles capable of supplying the ISS were grounded.
The decision to ground came after the Columbia disintegrated over Texas in February, killing all seven astronauts on board. The resulting report was damning of safety standards at US space agency, NASA.
The Progress rocket took off on Friday - ferrying food, water, fuel and oxygen.
Among the 2566kg cargo received by America’s Edward Lu and Russia's Yuri Malenchenko, are some less vital French and Russian comedy films, CDs with Russian Cossack songs, chocolate and a satellite telephone.
The craft also delivered scientific equipment for experiments by Spain's Pedro Duque, who will go up with US astronaut Mike Foale and Russia's Alexander Kaleri in October.
Malenchenko and Lu will come
back to Earth in October
Duque will return to Earth a week later with Lu and Malenchenko at the end of their six-month stint in space.
Russian cosmonaut Malenchenko managed a space first earlier this month by marrying his earthling fiancee by space phone.
Russia has borne the brunt of manned flights and supplies to the $95 billion, 16-nation ISS – and is the only country supplying the station’s crew and its rockets have an impressive reliability rate of up to 99%.
But senior Russian space officials say that while Moscow is coping with the technological part of the costly programme, it would welcome strong financial assistance from Washington.
NASA officials have so far estimated that next March or April is the soonest the shuttle can fly again, but as yet there have been no public talks on financial assistance.