The countdown had hit T-minus-0 at 4:55 a.m. in Cape Canaveral and the rocket appeared to light briefly before computers detected the problem and automatically shut down, the Los Angeles Times reported.
Elon Musk, SpaceX founder and CEO, posted on Twitter: "Launch aborted: slightly high combustion chamber pressure on engine 5. Will adjust limits for countdown in a few days."
The Hawthorne, Calif., company Space Exploration Technologies Corp. could next launch its Falcon 9 rocket Tuesday at 3:34 a.m.
With the space shuttle fleet now retired, the test launch of the unmanned SpaceX is to determine if the commercial rocket and space capsule can begin hauling cargo for the space agency.
SpaceX would become the first privately built craft to dock with the space station.
The company already has a $1.6-billion contract to haul cargo in 12 flights to the space station for NASA.