The largest rockets currently built by private companies are smaller than the Space Launch System, so if NASA decides on this approach, the payload for the mission would need to be split between two rockets. The Orion capsule and its service module, a component built by the European Space Agency to provide power and propulsion, would ride to orbit on one rocket. A fueled rocket stage for propelling Orion to the moon would go up separately.

The two pieces would then rendezvous and dock in orbit before heading to the moon. Mr. Bridenstine noted that Orion currently lacks the ability to dock with another spacecraft in orbit. “Between now and June of 2020, we would have to make that a reality,” Mr. Bridenstine said.

Senator Roger Wicker, Republican of Mississippi and chairman of the Committee on Commerce, Science and Transportation, noted: “This is 2019.”

A commercially launched mission would allow extended testing of Orion and the service module, one of the main goals, but it would push the first flight of the Space Launch System further into the future.

Mr. Bridenstine did not name which commercial rockets might be used, but the two that are powerful enough are the Delta 4 Heavy from the United Launch Alliance, a joint venture between Boeing and Lockheed Martin, and the Falcon Heavy from SpaceX, the rocket company founded by Elon Musk.

The Orion has been launched once already on top of a Delta 4 Heavy, in 2014, for a crewless test flight, but that did not go to the moon. The Falcon Heavy has only flown on its February 2018 test launch.

At the hearing, Mr. Bridenstine continued to describe the big NASA rocket as a core component of the space agency’s plans. But if the commercial approach works for the test flight, some space watchers wonder why the same strategy would not work for missions carrying astronauts.