In a speech Saturday to young Republicans, the Georgia business executive was silent about sexual harassment accusations that have jolted his presidential campaign. Four women have accused Cain of sexually harassing them when he led the National Restaurant Association more than a decade ago; two of them filed complaints. Cain has denied wrongdoing.
In his speech, Cain praised President John F. Kennedy as a "great leader" for inspiring a national effort to put a man on the moon, a goal achieved when astronaut Neil Armstong stepped onto the moon's surface in 1969.
"He didn't say, `We might.' He didn't say, `Let's take a poll,"' Cain said. "He said, `We will.' And we did. Only for this president to move us back by canceling a major part of our space program."
Cain also criticized Obama for using Russian technology to ferry astronauts and cargo to the International Space Station.
"I can tell you that as president of the United States, we are not going to bum a ride to outer space with Russia," Cain said to loud applause. "We're going to regain our rightful place in terms of technology, space technology."
Cain was talking about U.S. plans, now that the space shuttle is retired, to use Russian rockets to send astronauts to the International Space Station. In the meantime, NASA is focused on explorations deeper in space.
It was Bush who decided in 2004 to retire the space shuttle program. The Republican president still supported sending astronauts to the moon and Mars.
Obama, once in office, dropped the goal of a moon mission. Instead, NASA has plans to build a giant rocket capable of sending astronauts to an asteroid and eventually Mars. It wants to outsource to private companies the task of ferrying astronauts and cargo to the space station -- a job previously performed by the space shuttle.
Until private companies are ready, NASA will keep buying seats on Russian Soyuz capsules to get astronauts to the space station. The cost per person to fly on a Soyuz is expected to rise from $56 million to $63 million, which is still cheaper than flying on the shuttle.
Cain did not explain how he thinks the United States should explore outer space and did not take questions from reporters afterward.
Cain spoke in advance of a Republican debate Saturday in South Carolina focused on foreign policy.