Kent, Washington - After his space firm Blue Origin lost out in the bidding process to build NASA's first commercial lunar lander, Amazon founder Jeff Bezos is trying again to secure a contract.

In an open letter to NASA chief Bill Nelson published Monday, Bezos made an offer for Blue Origin to cover costs up to $2 billion this year and in the next two years for the development and production of a moon lander – if the company is allowed to compete again against Elon Musk's SpaceX.

NASA did not initially make any public response.

The space agency decided against Blue Origin in the April bidding process and instead awarded SpaceX the contract to develop the first commercial lander to take astronauts to the moon.

The contract is worth nearly $3 billion and forms part of NASA's Artemis program.

Since the decision was made, Blue Origin has protested it several times. Blue Origin's New Shepard spacecraft took Bezos on a short trip into space last week.

NASA's Artemis program, which aims to return astronauts to the moon by 2024 as a stepping stone to the first human mission to Mars.

The NASA mission will see four astronauts launched on NASA's Orion spacecraft into lunar orbit, where two of them will transfer to the SpaceX human landing system for their final journey to the moon.

The two astronauts will explore the lunar surface for around a week before returning to Earth.