NASA said in a statement it paused work with SpaceX on the human landing system through 1 November.
"In exchange for this temporary stay of work, all parties agreed to an expedited litigation schedule that concludes on 1 November," the US space agency said. "NASA officials are continuing to work with the Department of Justice to review the details of the case and look forward to a timely resolution of this matter."
The US Government Accountability Office (GAO) last month sided with NASA over its decision to pick a single lunar lander provider, rejecting Blue Origin's protest.
SpaceX, headed by Tesla Inc's CEO Musk, this week intervened in the lawsuit to ensure that the court "has a complete and accurate picture of the facts and circumstances surrounding this protest, including the substantial harm that SpaceX will suffer if the court grants the relief sought" by Blue Origin.
SpaceX did not immediately respond to a request for comment.
Blue Origin, the rocket company founded by Amazon.com Inc's founder Bezos, has said it remains convinced there were "fundamental issues" with NASA's decision and that the GAO was not able to address them "due to their limited jurisdiction."
NASA sought proposals for a spacecraft that would carry astronauts to the lunar surface under its Artemis program to return humans to the moon for the first time since 1972.
The space agency said on Thursday it "is committed to Artemis and to maintaining the nation's global leadership in space exploration. With our partners, we will go to the moon and stay to enable science investigations, develop new technology, and create high paying jobs for the greater good and in preparation to send astronauts to Mars."
In April, NASA awarded SpaceX a contract to build such a spacecraft as early as 2024.