Federal prosecutors investigating Boeing are examining whether the company knowingly misled the Federal Aviation Administration while it was seeking the regulator’s approval for its 737 Max plane, according to two people familiar with the matter who spoke on the condition of anonymity to discuss an active inquiry.

In recent months, prosecutors have questioned several Boeing employees in front of a federal grand jury, with some of their queries focusing on whether Mark Forkner, a top pilot at the company, intentionally lied to the regulator about the nature of new flight control software on the jet, the people said. That software, which is known as MCAS and automatically pushes the nose of the plane down, played a role in two crashes that killed 346 people.

The Department of Justice has been investigating Boeing for months, but the information about the grand jury testimony provides some clarity about how prosecutors could be aiming to hold the company accountable for errors that led to the crashes. Mr. Forkner could face criminal charges of lying to the government. The company could also be held liable for potential wrongdoing by Mr. Forkner, because he was a senior employee responsible for Boeing’s interaction with the F.A.A. group that determined the kind of training pilots would need before flying the Max.

Last year, the company made public an instant message chat between Mr. Forkner and his colleague Patrik Gustavsson. In the exchange, from November 2016, months before the F.A.A. certified the Max, Mr. Forkner said MCAS was acting unpredictably in a flight simulator. “I basically lied to the regulators (unknowingly),” Mr. Forkner said.