NASA is also seeking $132 million for developing technologies like converting ice within craters at the moon’s poles to water and $90 million for robotic exploration of the moon.

Mr. Bridenstine said that even higher increases would be needed in future years and that NASA was still figuring how much that would be. He described the current request as a “down payment.”

No cuts would be made to other NASA programs, said Mr. Bridenstine, who emphasized that the agency’s financing for the International Space Station and science programs would be secure. He added that he did not know what cuts might be made to other parts of the federal budget to pay for the moon program .

The proposed NASA increase is part of a larger budget amendment sent by the White House to Congress on Monday night. The extra money for NASA and other items would be financed from surplus Pell Grant money, an administration official said, but no students would lose aid as a result.

The budget amendment would take away another $1.9 billion from the Pell Grant program, the official said. Enrollment in the program has declined since 2011, leading to a surplus of $9 billion, the official said. Even with the proposed reduction, the program would have sufficient money to cover all costs through 2023, the official added.

Under the NASA plan, a mission to land on the moon would take place during the third launch of the Space Launch System. Astronauts, including the first woman to walk on the moon, Mr. Bridenstine said , would first stop at the orbiting lunar outpost. They would then take a lander to the surface near its south pole, where frozen water exists within the craters.