"The Human Landing System program needs competition, not the delay of starting over," Bezos' Blue Origin wrote. "The National Team has an open architecture, deep experience, massive self-funded investments and a safe, low-risk design to return to the Moon. Let’s go. #Artemis"
"For the low, low price of … ?" Musk retorted early Friday morning.
In turn, Blue Origin and "The National Team" filed a 50-page protest with the Government Accountability Office (GAO) over the decision in April.
Blue Origin CEO Bob Smith told The New York Times that the company believed NASA's selection was based on flawed evaluations.
Another competitor, Dynetics, also filed its own protest.
The GAO is conducting an investigation into the issue that is slated to conclude by Aug. 4.
This is not the first time the pair have taken to social media to face off publicly.
Previously, Musk had called Bezos a "copycat" after Amazon announced its intention to create a constellation of thousands of internet satellites and teased Bezos over Blue Origin's lunar lander, Blue Moon.