On Friday, astronauts closed a hole in the thermal blanket of space shuttle Atlantis. They also fixed two main computers aboard the ISS after an unprecedented 48-hour systems breakdown.
Brandy Dean, a Nasa spokeswoman said: "For now, it's working ... This is good news. It's very encouraging.
"The computers returned to full operation," Nasa said in a statement on Saturday.
Mike Suffredini, space station program manager, said: "I think we're in good shape ... We've got a talented group of people to look at attitude control."
Computers stabilise the station in orbit and manage critical oxygen and water supplies. Suffredini said the crew was not in danger.
"We are in a very good position from a life-support perspective ... We have plenty of oxygen on board," he said from the Johnson Space Centre in Houston, Texas.
Bill Gerstenmaier, Nasa associate administrator, said there was only "an extremely remote chance" that the problems could force the shuttle and ISS crews to abandon the station.
The astronauts completed the third of four planned spacewalks, with the most recent to repair a patch of thermal blanket to the rear of the shuttle.
The space walk, planned to last six hours and 30 minutes, lasted seven hours and 58 minutes.
Danny Olivas, an astronaut, used surgical staples to pin down a corner of the blanket, which came loose as the shuttle reached escape velocity from the Kennedy Space Centre on June 8.
Nasa engineers stressed that the hand-size opening posed no threat to the crew, unlike the broken tile that caused the Columbia to break up on re-entry in February 2003.
That disaster was caused by breaks in the shuttle's ceramic heat shield due to foam insulation peeling off its fuel tank and striking a wing during the launch.
Nasa has decided to prolong the mission two extra days until June 21 to make time for the repair.