The next launch opportunity opens May 11, with a slightly more than two-hour window starting at opening at 4:14 pm (2014 GMT) and ending at 6:21 pm.
"The vehicle and payload are in good health," said a SpaceX spokesman, who was unable to give a precise reason for the aborted launch at Cape Canaveral, Florida.
The rocket's main goal for its maiden mission is to propel the first high-orbit communications satellite for Bangladesh, called Bangabandhu Satellite-1.
Eventually, the rocket is slated to launch humans to the International Space Station, aboard SpaceX's Dragon crew capsule, still under development.
The first crew launch is tentatively planned for December 2018.
When that happens, it will mark the first time since the end of the US space shuttle program in 2011 that a rocket has launched from the United States carrying people to space.
"We expect there would be literally no action taken between flights, so just like aircraft," Musk said.
"It has taken us -- man, it's been since 2002 -- 16 years of extreme effort and many, many iterations, and thousands of small but important changes to get to where we think this is even possible," he added.
The Block 5 rocket is the final upgrade for SpaceX's Falcon 9 fleet. Next, the company plans to focus on its heavy-lift rocket, called BFR.
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