Discovery's most recent flight with the faulty part was in December on a rescue mission to the Hubble Space Telescope.
The problem may force the organisation to halt Monday's scheduled launch of the space shuttle Endeavour. Officials said they would take a decision on Sunday.
Nasa said on Saturday that a faulty turbine seal which should have been discarded was instead installed on Discovery.
Discovery's most recent flight with the faulty part was in December on a rescue mission to the Hubble Space Telescope.
The damaged component measures 3.5 inches by 0.5 inches (8.9cm by 1.3cm) and is part of a seal that forces hot gasses in the shuttle's three main engines through turbine blades.
"A scrap part got into a flight engine," shuttle programme manager Ron Dittemore said.
He added that there was very little chance that a similar mistake had been made on the Endeavour.
Wear and tear
Mr Dittemore said engineers only discovered the fault on Discovery because of some unusual signs of wear and tear during a routine servicing.
Had the joint given out during launch, the Discovery team may have faced an emergency landing.
Countdown continues
Nasa said the Endeavour launch countdown would continue while a decision was made on whether to postpone it.
The shuttle is set to take six astronauts - four Americans, a German and a Japanese - on an 11-day mission to produce the most complete three-dimensional map of the Earth's surface ever made.
The Shuttle Radar Topography Mission (SRTM) will produce the data with a 60m (196ft) radar mast - the longest rigid structure ever deployed in space.
Weather conditions are 70% favourable for the launch from Cape Canaveral, Florida, at 1747 GMT (1247 local) on Monday.
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