The Atlantis space shuttle mission will be extended from 11 to 13 days so that astronauts can attempt to fix a thermal blanket that peeled back during launch.
The repairs could be made during a planned third spacewalk or a fourth, extra one, Nasa managers have said.
Engineers think the blanket was loosened by aerodynamic forces during lift-off, and was not hit by debris.
Atlantis docked with the ISS on Sunday, after a back flip so that its underside could be inspected for damage.
Damage to the shuttle Columbia in 2003 during its launch led to the vehicle's disintegration as it returned to Earth, killing all seven crew.
A 10cm (4in) section of thermal blanket - which protects the shuttle from the intense heat of re-entering the atmosphere - peeled back as the shuttle blasted off from Cape Canaveral on Friday.
"It was a 100% consensus that the unknowns of the engineering analysis and the potential damage... under the blanket was unacceptable and we should go in and fix it if we could," said John Shannon, who chairs the mission management team.
Engineers do not think the re-entry heat could burn through the graphite structure underneath the blanket and jeopardise lives, but they are concerned it might cause some damage that would require repairs on the ground.
With three additional shuttle flights to the ISS planned this year, Nasa cannot afford any delays.
During the repair, an astronaut will probably reach the blanket, located near Atlantis' rear, by securing themselves to the end of the shuttle's robotic arm and boom.
On Monday, two US astronauts aboard Atlantis carried out a spacewalk to begin deploying new solar panels on the International Space Station (ISS).
The operation was delayed for several hours when four gyroscopes that keep the ISS steady became overloaded.
The space station's robotic arm had already attached a new 16-tonne (35,000lb) segment to the ISS containing a pair of new solar panels.
The panels will increase the station's power generation capacity, paving the way for Europe's Columbus module to join the station later this year.
Two more spacewalks, on Wednesday and Friday, are planned to finish installing the new solar array, with a fourth one a possibility - depending on how managers decide to carry out repairs.
This was supposed to be the second shuttle mission of 2007, but a freak storm over the Florida launch site in late February caused hail damage to the shuttle and delayed the mid-March flight.
Despite the delays, managers are confident they will be able to complete the ISS before the shuttles' 2010 retirement date.
Nasa plans to fly 15 more missions to the station to deliver large components, spare parts and other supplies. In addition, one final servicing call to the Hubble Space Telescope is planned for September 2008.