The United States is "very much in a space race right now" against China, NASA Administrator Jared Isaacman told CBS News' "Face the Nation" on Sunday, as the two nations attempt to land astronauts on the moon and secure a near-permanent presence on the lunar surface.

"The Chinese are moving at incredible speeds, and they are certainly capable of doing what the Soviets were not during the first space race," Isaacman said. "The Chinese will land their taikonauts on the moon. There's no question."

Isaacman stressed that "the question is, will the United States return before them, and will we do so in a different way this time, when we build a base, establish that enduring presence? I think the answer is yes."

After four astronauts looped around the moon on the Artemis II mission in April, NASA earlier this month announced the crew for the next Artemis mission, scheduled for next year, CBS News reported.

The Artemis III mission, which aims to test critical lunar landing systems, will be an important milestone before the U.S. sends astronauts back to the moon in 2028.

Isaacman told "Face the Nation" that on Artemis III, "You're going to see the three most powerful rockets in the world ... And then you're going to have the landers come together in Earth orbit, test out their capabilities, very a la Apollo 9, give us the confidence in our landers for Artemis IV in 2028. This is an achievable plan to put astronauts back on the surface of the moon."

Isaacman added that NASA will work on its moon base, with missions launched on a nearly monthly cadence in 2027 "so we have that enduring presence, that proving ground for Mars."

Isaacman predicted that starting next year, NASA could begin building the base. Then, when the astronauts get to the surface of the moon in 2028, he said "there's going to be a buggy there, a lunar terrain vehicle, there's going to be a start of infrastructure ... [and] I would say, early 2030s, the moon is going to be like the International Space Station. "

He emphasized that "you're going to have crews that are there on pretty extended periods of time, as we learn in that environment and prepare for Mars."