"Issue with Dragon thruster pods. System inhibiting three of four from initializing. About to command inhibit override," the company's billionaire founder Elon Musk wrote on the micro-blogging website Twitter.
SpaceX spokeswoman Christina Ra said the spacecraft "experienced an issue with a propellant valve" after reaching orbit.
"One thruster pod is running. We are trying to bring up the remaining three. We did go ahead and get the solar arrays deployed. Once we get at least two pods running, we will begin a series of burns to get to station," she said.
The malfunction occurred shortly after the capsule achieved orbit and separated from the Falcon 9 rocket that launched it earlier in the day from Cape Canaveral, Florida.
Before the technical difficulties the unmanned spacecraft had been scheduled to arrive at the International Space Station at 1130 GMT Saturday.
The Dragon vehicle is carrying 1,200 pounds (544 kilograms) of supplies on the firm's second resupply mission to the ISS. The two missions were preceded by a nearly flawless test mission.
The first resupply mission last October was a milestone in US efforts to cut costs by privatizing space exploration. The current mission is the second of 12 planned trips in NASA's $1.6 billion contract with SpaceX.
"This unique vehicle has become a very integral part of how we operate and use the space station," NASA's ISS program manager Mike Suffredini said on Thursday, as he described plans for the 25-day mission.
SpaceX president Gwynne Shotwell said that among the equipment on board are two grapple bars that will be transported in an unpressurized compartment of the spacecraft, a first for SpaceX.
Also on board will be equipment for 160 experiments to be conducted by the space station crew, which currently consists of two Americans, three Russians, and a Canadian.
On the return flight, Dragon -- the only spacecraft able to bring cargo back to Earth for now -- will be loaded with just over a ton of materials, including results of medical research.
The capsule is scheduled for a splashdown landing off the coast of California on March 25.
NASA has bet on SpaceX and other commercial ventures to take over for its retired fleet of space shuttles, which last flew in July 2011.
Before SpaceX's successful mission in October, NASA had been relying on Russian spacecraft -- but the Soyuz craft does not have room for cargo on the return flight.
SpaceX says it has 50 launches planned -- both NASA missions and commercial flights -- representing about $4 billion in contracts.
So far, SpaceX has only sent unmanned flights into orbit, but the company aims to send a manned flight within the next three or four years. It is under a separate contract with NASA to refine the capsule so that it can carry a crew.
NASA also has a $1.9 billion resupply contract for the station with Orbital Sciences Corporation, which will launch the first test flight of its Antares rocket from a base in Virginia in the coming weeks.