Blue Origin, the Jeff Bezos-founded U.S. space company, lodged a protest against NASA's choice of competitor SpaceX -  led by Elon Musk - to build the space vehicle that will transport the next American astronauts on the moon, Dodo Finance reported Wednesday.

Blue Origin filed a protest Monday to the Government Accountability Office, an agency that evaluates services for the U.S. Congress. The 50-page complaint shows that the billionaire Bezos and his aerospace allies are not backing down from the Government Accountability Office decision without a fight.

As this developed, Musk - chief executive officer of SpaceX - took a jab at rival billionaire Bezos' Blue Origin in the face of a showdown over the nearly $3 billion contract to build a lunar lander for NASA.

In a tweet, Musk responded to the report about Blue Origin's protest by making a thinly veiled joke about the male reproductive system: "Can't get it up (to orbit) lol."

On April 17, NASA granted SpaceX a $2.89 billion contract for exclusive rights to build a moon lander to use in its flagship mission of the decade.

In a statement sent to Agence France-Presse, Blue Origin said: "NASA has executed a flawed acquisition for the Human Landing System program and moved the goalposts at the last minute."

"Starship has no flight heritage or validation of performance, and launch vehicle development is notoriously difficult and takes much longer than anticipated," Agence France-Presse quoted Blue Origin as saying in the complaint.

The lunar vehicle is the third major part of the Artemis missions - the name given to NASA's revived lunar explorations program which ended five decades ago with the Apollo missions.

Under the current blueprint, NASA is looking to send two astronauts - a man and a woman - to the moon's surface at some point in 2024.

That Blue Origin and SpaceX are on collision course is hardly surprising: Bezos and Musk have very deep pockets and are both obsessed with expanding humanity's presence in space.