Pence's announcement took many inside NASA by surprise.
"No woman has ever walked on the lunar surface". And in March, the White House submitted a budget request totaling just over US$21 billion for Nasa, a almost US$500 million cut of what the agency received this year.
The revised plan from NASA calls for launching components of the small, space-station-like Lunar Gateway on commercial rockets by 2024.
At the moment, Nasa now does not have the ability to fly astronauts anywhere in space. Instead, it pays Russian Federation more than $80 million a seat to fly its astronauts to the International Space Station.
The increased funding request, announced by President Donald Trump on Twitter, comes almost two months after Vice President Mike Pence declared the objective of shortening by four years NASA's previous timeline for putting astronauts back on the moon for the first time since 1972.
An allotment of $US651 million ($936 million) will be used to support the Orion Spacecraft and the rocket that Boeing is building for the moon mission - called the Space Launch System or SLS.
NASA announced Mr Trump challenged the agency to land at the south pole of the moon by 2024.
In a tweet Monday evening, President Trump wrote: "Under my Administration, we are restoring @NASA to greatness and we are going back to the Moon, then Mars". It's the boost NASA needs, allowing us to move forward with design, development and exploration.
But Nasa officials warned that it would need additional money in the future in order to meet the goal.
Use of the Pell Grant money to fund the moon mission, dubbed Aretmis, would "cut any spending for for Pell Grant programs as the budget continues to ensure all students will get their full Pell Grant and keeps the program on sound fiscal footing", Office of Management and Budget spokesman Wesley Denton said in a statement, according to the AP. "This is a good amount that gets us out of the gate in a very strong fashion, and sets us up for success in the future". And he said America can't do that without what it learns by going back to the Moon first. Still, to meet the five-year goal, NASA has said it would scale back the scope of the Gateway, at least initially. To accommodate getting humans to the surface quickly, the budget amendment proposes cutting $321 million from that project and shifting "potential Gateway capabilities into the future".
Officials insisted the re-allocation of the Pell Grant money would have no impact on those now receiving grants, which help low-income students pay for college.
In the call, Bridenstine and others emphasized that, other than the cut in proposed Gateway funding, no other NASA programs were reduced to support this funding increase.
It is not clear what the reaction in Congress would be. Bridenstine said he had been reaching out to key Congressional leaders but that it was "not easy to get a hold of everyone" on short notice.
"The next leap in space will be fueled by commercial companies changing the way we do business in space while creating new technologies and innovations", he said. "I think there's a lot of excitement on both sides of the aisle", he said. That would be followed by another mission, with astronauts in the Orion crew capsule, for a trip around the moon.
NASA is planning on sending the first woman ever and the first man in almost five decades to the moon by 2024, thanks to an additional increase to the agency's budget by US President Donald Trump.
"Our goal here is to build a program that gets us to the Moon as soon as possible that all of America can be proud of", he said.
But at a recent congressional hearing, Bridenstine disputed that.
Bezos, the richest person in the world and founder of Amazon.com Inc, last Thursday unveiled his space company's mock-up of a lunar lander being built by Blue Origin, the latest company after Lockheed Martin and Boeing to do so.