Japanese astronaut Soichu Noguchi and American mission specialist Stephen Robinson opened a hatch leading to the outside of the Discovery-International Space Station complex at 8.48am GMT (6.48pm AEST).
The pair are attaching a stowage platform and a material science experiment to the International Space Station, where Discovery is currently docked, and are retrieving a faulty heat dissipater, as well as tackling the fibre removal operation.
Mr Robinson is attempting to remove two protruding tile gap filler fibres with a pair of forceps or a hacksaw if needed.
“I am pretty comfortable with using tools very carefully,” said the astronaut in a press conference from the Discovery on Tuesday.
“But no doubt about it, this is going to be a very delicate task. But as I say a simple one.”
Deputy shuttle programme director Wayne Hale said that if the hacksaw is not successful, another spacewalk could be organised for Thursday or Friday.
There are fears the protruding fibres could cause the shuttle to overheat due to instability between thermal tiles on the shuttle’s underside.
The fibres break the smooth contour of the underbelly, which is essential for a problem-free re-entry into the Earth’s atmosphere.
It is the first time such an operation has been undertaken, and Australian crew member Andy Thomas said astronauts initially had misgivings about going underneath the shuttle.
“We were concerned about it — we were concerned about the implications of it and what was motivating it,” he said on Tuesday.
He said NASA engineers have also been analysing a thermal blanket below the Discovery’s cockpit, which apparently was hit by debris during liftoff on July 26.
“I have people who will come back and report within 48 hours, so I will get a status report tomorrow,” said Mr Hale, adding that there is some concern the blanket might tear off during re-entry.
The shuttle is scheduled to leave the space station Saturday and return to Earth early on August 8.