The Sept. 18, 1963, conversation is among 260 hours of White House recordings that archivists at the John F. Kennedy Presidential Library and Museum have been reviewing.
The release of the recordings on Wednesday comes on the 50th anniversary of Kennedy's May 25, 1961, speech in which he made his famous call to reach the moon by decade's end.
Two years after that speech, Kennedy and NASA Administrator James Webb were recorded talking about their worries about a massive program that is not making obvious advances.
"I don't think the space program has much political positives," Kennedy tells Webb.
The president seems to lament that the rival Russians haven't made the progress in their half of the space race that could bring needed attention to America's program.
"I mean if the Russians do some tremendous feat, then it would stimulate interest again, but right now space has lost a lot of its glamour," Kennedy said.
Webb acknowledges that the tens of billions of dollars spent over a decade made the program a target for lawmakers. But he repeatedly pushes its merits, including spurring technological advances he says will vastly expand the country's economic might.
"I think it's going to generate the technology that's going to make a difference for this country far beyond space," Webb says.
At one point, Kennedy asks Webb, "Do you think the lunar, manned landing on the moon is a good idea?" The president also asks for and receives assurances from Webb that sending a man to the moon isn't just a "stunt" that will yield the same advances as sending scientific instruments to the moon's surface for billions less.
Kennedy and Webb then agree it's crucial to emphasize the space program's importance to the military and national security, or risk it being considered wasteful.
"The heat's going to go on unless we can say this has got some military justification and not just prestige," Kennedy says.
"I think it's the only way we're going to be able to defend it before the public in the next 12 months," Kennedy says. "I want to get the military shield over this thing."
John F. Kennedy Presidential Library and Museum archivists said the tape offers a look at the pragmatism behind Kennedy's vision for America's future in space.
The Associated Press contributed to this report.