Atlantis, carrying a six-member crew, lifted off from Cape Canaveral, Florida, on Saturday.
"I have not seen a single problem with the vehicle, and the crew is ahead of schedule," said shuttle flight director Paul Dye, speaking after astronauts reported finding no damage to the craft's heat shields from debris.
"So far, everything has gone exactly according to plan," Mr Dye told reporters at the Mission Control Centre at the Johnson Space Centre in Houston.
The astronauts used the orbiter boom sensor system, attached to the end of the shuttle's robot arm, to closely inspect the wing leading edges and the nose cap, NASA said.
Later the crew will detach the boom and use the arm's camera to inspect the crew cabin and other areas on Atlantis. Another heat shield inspection will take place after undocking from the ISS.
Wayne Hale, NASA space shuttle program manager, said earlier that high definition television footage of the lift-off showed several pieces of debris -- apparently foam and ice -- breaking off and possibly impacting the orbiter.
Foam shed during launch caused the 2003 space shuttle Columbia disaster.
Columbia disintegrated upon re-entry into the Earth's atmosphere because a piece of loose foam insulation had pierced the shuttle's protective heat shield during take-off.
The two shuttle flights conducted since then were focused on correcting the problem and improving flight safety. After Discovery returned in July from its latest mission, NASA declared it was ready to resume construction of the ISS.
Atlantis was supposed to launch on August 27, but the mission was postponed five times due to a lightning strike, a looming tropical storm and technical glitches.
National Aeronautics and Space Administration officials said the 11-day mission to boost power on the ISS entails the most complex work ever undertaken at the nearly eight-year-old, half-finished orbiting laboratory.
Completing the space station is central to US ambitions to fly humans to Mars.
The shuttle is scheduled to dock with the ISS at 6:46 am (1046 GMT, 2046 AEST) Monday.
The Atlantis crew began their first full day in space at 0515 GMT on Sunday with a wake-up call from the Mission Control Centre.
Atlantis is transporting a 16-tonne segment with two huge solar panels that will double the space station's ability to produce power from sunlight and ultimately provide a quarter of the power for the completed ISS.
Three spacewalks are planned for the construction work.
The Atlantis crew is commanded by Brent Jett and co-piloted by Chris Ferguson. The four mission specialists are Daniel Burbank, Heide Stefanyshyn-Piper, Joe Tanner and Canadian Steve MacLean of the Canadian Space Agency.
NASA plans 15 more shuttle trips to complete the orbiting laboratory by 2010, when the three-shuttle fleet is to be retired.