The Soyuz TMA-3 lifted off from Baikonur cosmodrome on Saturday for a 200-day mission with a Russian, an American and a Spaniard on board. It is due to dock with the 16-nation orbital platform on Monday.
"This is a very historic day. It again demonstrates the depth of commitment to this partnership," NASA Administrator Sean O'Keefe said after the launch.
With US space shuttles still grounded after the Columbia disaster early this year, the International Space Station's survival depends on Russian spacecraft.
"Russian cosmonauts and Russian space authority Rosaviakosmos are carrying the substantial load of maintaining the space station," O'Keefe said.
Family and friends of the crew members watched the launch on screen in the observation area, before bursting into applause.
Funding concerns plague the International Space Station, with Russia launching all manned and supply ships to the station since February.
O'Keefe said Russia should press on with its commitment while the US worked to bring the shuttle back into service.
"This is a very historic day. It again demonstrates the depth of commitment to this partnership"
"All the expense and resources the American people are putting into returning the Shuttle to flight, we have no intention of passing these bills across to any of our partners," he said.
Russia says it needs more money and has started sending space tourists to the station at a fare of $20 million to help cover the cost of building new Soyuz craft.
Uncertain finances could prompt a delay in the launch to the International Space Station of the next Progress cargo ship from November to January.