Russian cosmonaut Sergei Krikalev and American John Phillips were headed for a six-month stay on the ISS, while their colleague from the European Space Agency, Italian Roberto Vittori, was due to return to Earth in 10 days with the current station crew.
Russian Salizhan Sharipov and American Leroy Chiao have been on the orbiting lab since October.
Jets of fire and billows of smoke accompanied the liftoff, which was being monitored at Russian Mission Control outside Moscow. The three-stage rocket system was to bring the Soyuz to a speed of 13,420 mph within 7½ minutes of the launch.
A main task for the new crew will be welcoming a U.S. space shuttle to the station after a two-year absence.
Vittori, flying for the European Space Agency, will stay eight days and return April 25 with Russian Salizhan Sharipov and American Leroy Chiao, who have been aloft since October.
Since the Columbia disintegrated upon re-entry on Feb. 1, 2003, shuttle flights have been suspended, leaving the Soyuz the only way of getting astronauts to the station. NASA aims to revive flights as early as May 15, with a mission by Discovery to the station.
The Columbia disaster was due to a failure of insulating tiles on the shuttle's exterior, which undergo extreme heat on both takeoff and landing. A key task for Krikalev and Phillips will be to observe the condition of the tiles on Discovery.
"Our particular part will be conducting a photo survey of the exterior of the shuttle while it is maneuvering immediately below us prior to docking," Phillips said at a news conference before the blast off.
"I think the eyes of the world are going to be upon the shuttle crew at that moment, and will be a little on us too, and I'm really proud to be a part in that," he said.
Krikalev said he expected to be moved by the shuttle arrival.
"When the shuttle comes, it will be a big celebration. They're not only bringing material for experiments, material for the station, food, water, gas, but they're bringing emotions," he said, speaking like the others from behind glass in a separate room to avoid contamination.
Although Vittori won't be aboard for the shuttle arrival, he expects to spice up the space station's cuisine.
"One of the particularities of this mission is that we also have some food coming from Italy," he said. "The idea is to bring a little flavor of Italy to the International Space Station."
Phillips, whose 54th birthday is Friday, said he's not overwhelmed by the rigors of space flight at his age and that others in their 50s and 60s shouldn't be either.
"I actually think I'm a pretty young man," he said.
Krikalev, 46, is one of the most experienced space flyers, having made missions both to the ISS and the Russian space station Mir. At the end of the new mission, he will have spent more time in space than any human, more than 800 days.
Along with preparing for the shuttle's return, experiments to be conducted during the long-term mission on the station include looking into muscle loss in space, kidney stones and radiation damage to chromosomes.
By Jim Heintz