Last week, NASA had cleared SpaceX for launch on April 30, pending a final review of its flight software, which will delay the mission one week, SpaceX said.
"Am pushing launch back approximately a week to do more testing on Dragon docking code. New date pending coordination with NASA," SpaceX founder Elon Musk wrote in a Twitter post.
SpaceX has a contract with NASA to fly cargo to the space station following the retirement of the space shuttles last year.
In December 2010, a SpaceX Falcon 9 rocket carried the company's Dragon capsule into orbit on a demonstration flight.
In the upcoming launch, a Dragon capsule will approach the space station and test its ability to maneuver in orbit, and if the testing is considered successful, NASA will clear the capsule to dock with the ISS.
"There's no space station on the ground, so our work to date has been done by simulation and by approximating the circumstances that it will find in orbit and approaching the space station. This is pretty tricky," Musk said last week.
A new launch date is expected to be announced later this week.