Just before explosion, Buzz Aldrin praises SpaceX's Elon Musk

Buzz Aldrin on the future of space

The future of the U.S. space program should rely more heavily on private companies than government resources, Apollo 11 astronaut Buzz Aldrin told CNBC on Thursday morning.

"Elon Musk's SpaceX rockets are cheaper than government rockets," the second man to walk on the moon said on "Squawk Box."

Aldrin's comments were made shortly before Thursday's explosion of a SpaceX rocket on the launch pad at Cape Canaveral. It happened during a test firing two days before planned liftoff. No injuries were reported, but the Falcon 9 rocket and its payload were destroyed.

The evolving business model for space exploration and travel is being led by three billionaires: Musk and SpaceX, Amazon founder and entrepreneur Jeff Bezo's Blue Origin, and Richard Branson's Virgin Galactic.

The new space race has a "long ways to go," Aldrin said. "We are still planning on to go to the moon and Mars on government rockets. I think it's time we need to entertain a change ... [in] who makes the cheaper rockets for the American people."

"[Private] is still cheaper than government transportation," he added.