A NASA official said the seven-member crew inspected Discovery's nose and wings for damage with a special robotic arm, concerned that loose foam that broke loose of the craft a few minutes into the launch may have caused some exterior damage.
"We have a very clean vehicle," shuttle flight director Tony Ceccacci said of the initial safety check, which came on the first full day of orbit.
The mission to the International Space Station is only the second NASA space flight since the Columbia disaster in February 2003.
Then a piece of loose foam pierced the shuttle's heat shield, causing it to disintegrate upon re-entry into the Earth's atmosphere, killing all astronauts on board.
NASA said the Discovery crew is working hard to complete the safety check in 24 hours and that initial indications are all good.
"It will take about eight to 10 hours to get a very good look at the first part of the survey and we should have ... that completed within 24 hours," Mr Ceccacci said. "Everything seems to be clear."
NASA appeared pleased with the performance of Discovery's external fuel tank, which lost only small pieces of foam insulation on Tuesday, without posing any serious threat to the shuttle's heat shield.
A Discovery flight last year was the first to use the new inspection procedures, which involve a robotic arm equipped with cameras and a laser to check on the shuttle.
The cameras and laser are capable of detecting damage as small as a third of a centimetre.
Shuttle backflip
The crew - Commander Steven Lindsey, pilot Mark Kelly and mission specialists Michael Fossum, Lisa Nowak, Stephanie Wilson, Piers Sellers and European Space Agency astronaut Thomas Reiter of Germany - focussed on the protective heat shield on the shuttle wings' leading edge.
When the vehicle gets closer to the International Space Station on Thursday, it will perform a backflip so that the ISS crew can further inspect the shuttle's heat-resistant surfaces, particularly on its belly.
The astronauts will then configure their spacesuits in preparation for two or three spacewalks after the shuttle docks with the ISS.
Reiter will join the ISS's two other crew members, Commander Pavel Vinogradov of Russia and Flight Engineer Jeffrey Williams, for a long-term stay and will undertake two spacewalks.
This week's Discovery launch is the 115th flight of the American shuttle program, and will deliver almost 13 tonnes of equipment and supplies to the ISS.
NASA officials have struggled to fix problems associated with the persistent loss of foam insulation since the debris doomed Columbia.
Foam fell off Columbia's fuel tank 70 seconds after liftoff, piercing its heat shield.
Foam also peeled off Discovery's tank in the first post-tragedy launch last year, but the debris missed the shuttle.
Nevertheless, NASA grounded the 25-year-old fleet until now to make further modifications.
NASA placed more than 100 cameras around Discovery's launch pad for Tuesday's liftoff to detect any loose debris.
The agency had said the seven astronauts could take refuge at the ISS and wait for a rescue mission in the event the shuttle has suffered irreparable damage.
Discovery is due to return to Earth on July 16.