The rocket lifted off at 3:02 a.m Thursday (2102 GMT Wednesday) and was to dock with the orbiting laboratory about six hours later. It reached orbit about 15 minutes after launch and is to circle the Earth four times before heading for the space station, which is about 250 miles (400 kilometers) above the Earth.
The capsule is carrying Oleg Kononenko of Russia, NASA's Kjell Lindgren and Kimiya Yui of Japan. Lindgren and Yui are on their first trips into space. Yui told a news conference that he was taking some sushi with him as a treat for the others.
They will join Gennady Padalka, Mikhail Kornienko and Scott Kelly. The latter two are more than four months into a nearly year-long mission on the space station.
The launch was postponed by about two months after the April failure of an unmanned Russian cargo ship, which raised concerns about Russian rocketry. Another Russian cargo ship was successfully launched in early July.