The second stage of the rocket failed 139 seconds after takeoff, after the first stage performed normally, SpaceX President Gwynne Shotwell said at a NASA news conference.
"We are working to identify the issue, to fix it, and get back to flying.''
Amid items lost were a docking adapter, a space suit and important experiments, NASA officials said.
"We lost a lot of research,'' one said, including student experiments.
SpaceX founder Elon Musk tweeted that an upper-stage liquid oxygen tank had "an overpressure event'' and the "data suggests (a) counterintuitive cause.''
Another supply mission, atop a different company's Progress launch vehicle, is scheduled for launch July 3. NASA officials said there was sufficient food, water and fuel on board the ISS for the time being.
At 7:21 a.m., a SpaceX Falcon 9 rocket carrying a Dragon capsule loaded with 4,300 pounds of goods was launched from Cape Canaveral, Florida. At first stage separation, 2 minutes and 19 seconds into the flight, it disintegrated.
More than 3,000 employees, most in the South Bay, work on SpaceX's new reusable space delivery system, designed to replace the now-retired fleet of Space Shuttles. SpaceX is one of two private U.S. firms with NASA contracts to deliver groceries and scientific equipment to the International Space Station in low Earth orbit.