The rocket, designed as a budget launch system for satellites and supplies for the International Space Station, was launched yesterday but failed to achieve the correct orbit.
Tracking problems in the second stage of the rocket caused it to lose course, but the firm is confident that it can fix the problems and complete a commercial satellite launch later this year.
"Falcon flew far beyond the 'edge' of space, typically thought of as around 60 miles," said the company.
"Our altitude was approximately 200 miles, which is just 50 miles below the International Space Station.
"The second stage did not achieve full orbital velocity due to a roll excitation late in the burn, but that should be a comparatively easy fix once we examine the flight data."
Musk started the SpaceX project to slash the cost of getting materials into space. Commercial satellite launches can cost as much as $10,000 per pound to launch into orbit, but SpaceX has the goal of bringing this below $1,000.
So far the company has $200m in orders for launches and has been hired by Nasa to deliver cargo and crew to the International Space Station.
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