The Soyuz-FG rocket soared into a darkening sky above the Kazakh steppe.
Aboard were Peggy Whitson of Beaconsfield, Iowa; veteran Russian cosmonaut Yuri Malenchenko; and Dr. Sheikh Muszaphar Shukor, the ninth Muslim in space but the first from Malaysia.
The mission coincides with the last days of Ramadan, the holy month when Muslims fast from dawn until sundown, but Malaysian clerics decreed that Shukor will be excused from fasting while in space.
His religion also requires that he face Mecca for prayer - a direction that will change as the craft orbits the Earth - but clerics decided that the exact location matters only for the beginning of the prayer ritual.
Shukor, who will return to Earth on Oct. 21, won a competition to become the first Malaysian in space after the Russians offered a space trip as part of a fighter jet sale to island nation.
"Being a Muslim and going to space is a big responsibility for me, not only for the Malaysian people but all the Muslims all over the world," Shukor said at a pre-flight news conference. "I'm sure I'll find a way how to pray and fast in space and I'll come back and I will share it with all the rest of the Muslims all over the world."
Whitson and Malenchenko will stay on as the station's new crew, and will be joined in October by U.S. astronaut Daniel Tani, who is arriving with the shuttle Discovery. Tani will replace fellow American Clayton Anderson, who has been at the station since June.
CBS News space consultant Bill Harwood reports Whitson, a station veteran who will become the first female to command the orbiting lab complex, was jokingly presented with a ceremonial whip during a final news conference "for the men to remember that you are the boss."
"Are you going to use it? Or are you going to be a nice commander?" someone else, presumably a reporter, asked in Russian.
"I'm hoping that I will not be needing this," Whitson laughed, according to a translator. "But just in case ..."
If all goes well, the Soyuz TMA-11 spacecraft will dock with the international space station around 10:52 a.m. Friday.
Whitson spent six months aboard the space station in 2002 as a member of the fifth expedition crew. Malenchenko is a veteran of three space missions including a visit to the old Mir space station, a shuttle flight and as commander of the space station's seventh crew.
Whitson and Malenchenko will replace Expedition 15 commander Fyodor Yurchikhin and flight engineer Oleg Kotov. Both men were launched to the station aboard a Soyuz on April 7. Expedition 15 science officer Clay Anderson, who was launched to the station aboard the shuttle Atlantis June 8, will remain aboard the outpost with Whitson and Malenchenko until his replacement - Dan Tani - arrives at the end of the month aboard the shuttle Discovery.
"I think that the Russians ... are a little further away from our perspective of what the woman's role is," Whitson said in a recent interview. "Knowing other cosmonauts, knowing the trainers, once you get to know them and once you're a part of their lives, they have accepted me in my role and it's very satisfying to me to have them accept me in spite of the fact that culturally, it's not necessarily the norm there.
"And I hope I can influence that as well. But launching on the Soyuz is probably going to be part of that role. And I think being commander is going to be noticed in Russia as well, a female commander."
By coincidence, shuttle Discovery will be commanded by Pam Melroy, a veteran shuttle pilot making her first flight as commander. In another coincidence, Melroy and her crewmates - Tani, pilot George Zamka, Stephanie Wilson, Scott Parazynski, Italian astronaut Paolo Nespoli and Doug Wheelock - planned to strap in aboard Discovery for a dress-rehearsal countdown about an hour before Whitson's launch.