SpaceX said it has pitched NASA a "simplified mission" to put astronauts back on the moon following criticisms over delays by Sean Duffy, the space agency's acting administrator.

"We've shared and are formally assessing a simplified mission architecture and concept of operations that we believe will result in a faster return to the moon while simultaneously improving crew safety.

Elon Musk's SpaceX on Thursday said it proposed to NASA a simplified plan to send humans to the moon using its Starship rocket, as the agency presses its contractors to move more quickly toward beating China to the lunar surface this decade.

SpaceX posted a response to criticisms of delays in its Starship program from NASA acting Administrator Sean Duffy.

SpaceX defended Starship and said it is assessing a simplified moon mission architecture, with a propellant transfer test next year.

NASA's chief said recently he's reopening bids for the Artemis III contract that it awarded SpaceX in 2021. SpaceX has now responded.

Elon Musk's SpaceX ( SPACE) and Jeff Bezos' Blue Origin ( BORGN) have submitted plans to NASA for ramping up efforts to take astronauts to the moon, the agency told CNBC. NASA "has received and is evaluating plans from both SpaceX and Blue Origin for acceleration of HLS [Human Landing System] production," a spokesperson for the agency said.

Former NASA officials warn that the U.S. looks poised to lose its self-declared race to beat China to the moon

Interest in the moon has been high—just in the past two years there have been 12 attempts to send missions to the moon, nearly half of which private companies undertook. With so much activity, it's important to start thinking about coordination and safety.