A final judgment is not expected until Monday. Nasa is still analysing the reinforced carbon protection for the nose cone and wing leading edges, and studying whether protruding gap fillers on the bottom of the spacecraft pose a significant risk, officials said.
National Aeronautics and Space Administration shuttle flight director Paul Hill on Sunday said that astronauts could be asked to fix the two pieces of filler dangling from Discovery's underbelly during a spacewalk.
"We have a team of folks working aggressively at options to go and make that gap filler safe if we decide it's an issue," Hill said from mission control at the Johnson Space Centre in Houston, Texas.
The fillers are used to keep hot gas from flowing into gaps in the thermal protection in tile-protected areas.
Nasa engineers and mission managers, meanwhile, have given Discovery's tiles the all clear following worries that they may have been damaged by a piece of insulating foam which fell off the rocket during lift-off on Tuesday.
A couple of short strips of material dangling from Discovery's belly had Nasa scrambling to determine whether the protrusions might endanger the shuttle during next week's descent and whether the astronauts might need to attempt a repair.
"We have a team of folks working aggressively at options to go and make that gap filler safe"
Nasa shuttle flight director
The potential trouble has nothing to do with foam or other launch debris - for a change - but rather the accidental slippage of material used to fill the thin gaps between thermal tiles.
It would be on Monday before the analysis is complete and mission managers decide whether to have the crew's two space walkers cut, pull out or shove back in the hanging material, Hill said.
Since the launch they have been reviewing images of Discovery's body to check for potential damage to avoid a repeat of the Columbia space shuttle tragedy in 2003.
The Columbia disaster was blamed on similar debris that hit the shuttle during blastoff.
Nasa officials were distraught to see the insulating foam fall off, since they had worked furiously to avoid such a problem.
Nasa administrator Michael Griffin said pre-flight safety checks had fallen short.
"Our judgement at the time was that it was okay. As everyone has said without any attempt to hide it ... we goofed on that one," he told NBC television.
Griffin also conceded Nasa had been "lucky" that the stray shard of foam that fell off Discovery's external tank during lift-off had not caused serious damage.
"If it had broken off earlier and if it had followed a different trajectory, it could have hit the orbiter... and could have done some damage," he said.
Columbia burned up during re-entry on 1 February 2003, after debris hit its left wing during lift-off, opening up a critical breach in the ceramic tiles that made up its protective heat shield.
A Nasa manager explains where
a window covering fell off
The seven crew members died. Nasa grounded its shuttle fleet and implemented major safety reforms after the tragedy.
The shuttle fleet was grounded again Wednesday after the foam debris fell off Discovery.
Discovery is currently docked at the International Space Station and the crew continued their mission on Sunday, moving supplies and equipment onto the station.
Japanese astronaut Soichi Noguchi and American counterpart Steve Robinson meanwhile prepared for their second spacewalk planned for Monday. They will install a 270-kg gyroscope on the ISS.
The pair tested new repair techniques during their first venture into space on Saturday. Discovery will spend an extra day in orbit, Nasa announced. The shuttle will now return on Monday, 8 August, at 0847 GMT, instead of Sunday.
The extra day in orbit will allow the seven-astronaut crew to get a head start on tasks that could be affected by the suspension of further flights: Removal of trash and old equipment from the space station.
Some 11 tonnes of waste have piled up over three years, cramping the space station. Astronauts will pack it into the Rafaello transport module which rides in Discovery's cargo bay and which had carried 13.5 tonnes of food and equipment for the space station.
First launched in August 1984, the shuttle has completed 30 successful missions in space, more than any other orbiter in the Nasa fleet.