This story was updated at 4:45 p.m. ET.

The private spaceflight company SpaceX will likely postpone the planned launch of its Dragon capsule to the International Space Station next week, officials announced today (May 2).

SpaceX was targeting the launch for Monday, May 7, but now will likely shift to a later date, possibly May 10. The unmanned Dragon spacecraft is due to lift off atop a SpaceX Falcon 9 rocket from Cape Canaveral Air Force Station in Florida.

"At this time, a May 7th launch appears unlikely," SpaceX spokeswoman Kirstin Brost Grantham wrote in a statement. "SpaceX is continuing to work through the software assurance process with NASA. We will issue a statement as soon as a new launch target is set."

The Dragon mission will be be the very first visit of a privately built spacecraft to the International Space Station. During the test flight, the spacecraft will carry food, supplies and scientific equipment for the astronauts living on the orbiting outpost.

The flight was previously delayed from an April 30 launch date to allow more time for tests of Dragon's flight software. The new delay is also meant to allow for further checkouts.

SpaceX conducted a test firing of its Falcon 9 booster engines April 30. The test went successfully on its second try, after a first attempt that same day was stalled by an apparent computer glitch.

SpaceX has a $1.6 billion contract with NASA to fly 12 cargo-delivery missions to the space station with Dragon. The capsule is scheduled to be the first spacecraft to fly under NASA's Commercial Orbital Transportation Services (COTS) program, which has funded the development of private vehicles to fill the gap in cargo services left by the space shuttle retirement.