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.

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.