"I made it possible for them to do this," Trump told Fox News as he took credit for the improvement of space programs and the private sector investment in the forward movement.
"I actually said to my people: Let the private sector do it," he told Sunday Morning Futures host Maria Bartiromo in a phone-in interview. "These guys want to come in with billions of dollars. Let's lease them facilities because you need certain facilities to send up rockets, and we have those facilities."
"We have the greatest. And I reopened them because they were, as I told you, they were dead, they were closed, or essentially closed for the most part."
The ex-president's remarks come as Branson, an English business magnate with a net worth of $5.9 billion, went to space in his own spaceship.
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"Better him than me. I would rather see Richard in the plane today than me in the spaceship," Trump told Bartiromo. "But if Richard loves it, and Bezos loves it, and a lot of rich guys love space."
Branson, nearly 71, beat out Amazon founder Jeff Bezos in getting to space.
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"So I said, hey look, if Elon wants to stand up a rocket, let him do it," Trump proceeded. "We'll charge him some rent. Let him do it. Let these guys do it."
"And we're seeing advancement now that I don't believe we would have ever seen had we done it the old-fashioned way," Trump said on Fox.
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Branson took along five crewmates aboard who are part of his Virgin Galactic space-tourism company.
The group attained an altitude of about 53 miles above the New Mexico desert - enough to undergo three to four minutes of weightlessness and see the shape of the Earth - and then safely glided to a runway landing.
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"The whole thing, it was just magical," a jubilant Branson said after the trip home aboard the gleaming white space plane, named Unity.
The brief, up-and-down flight - the rocket ship's part took only about 15 minutes, or about as long as Alan Shepard's first U.S. spaceflight in 1961 - was a splashy and unabashedly commercial plug for Virgin Galactic, which intends to start taking paying customers on joyrides next year.
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Branson became the first character to go in his own spaceship, beating Bezos by nine days. He also became only the second septuagenarian to go into space. Astronaut John Glenn flew on the shuttle at age 77 in 1998.
Bezos sent his compliments, adding: "Can't wait to join the club!" - though he also took to Twitter earlier in the week to identify the ways in which he believes his company´s trips will be better.