A senior Boeing executive has said he may have “unknowingly” misled US regulators about the software program linked to two fatal crashes of 737 Max airliners.

The Federal Aviation Administration (FAA) confirmed on Friday that Boeing told it a day earlier about internal messages it had discovered “some months ago” that characterize “certain communications with the FAA during the original certification of the 737 Max in 2016”.

The FAA said it found the messages “concerning” and “is reviewing this information to determine what action is appropriate”. It prompted a letter from the FAA administrator, Steve Dickson, to Boeing’s chief executive, Dennis Muilenburg, demanding an “immediate” explanation for the delay in turning over the documents.

A person briefed on the matter said Boeing failed to turn over the documents to the FAA for four months and that the justice department is also in possession of the messages.

The Boeing internal messages raised questions about the performance of the so-called MCAS anti-stall system that has been tied to the two fatal crashes in five months.

The messages are between the Max’s then chief technical pilot, Mark Forkner, and another Boeing pilot, the sources said, and raised questions about the MCAS’s performance in the simulator in which he said it was “running rampant”.

Forkner has since left Boeing. The Seattle Times reported in September that Forkner repeatedly invoked his fifth amendment right to not turn over documents subpoenaed by the justice department.

Boeing said in a statement the company “brought to the committee’s attention a document containing statements by a former Boeing employee”.

Forkner said in one text message, “I basically lied to the regulators (unknowingly).” The other employee responded that “it wasn’t a lie, no one told us that was the case” of an issue with MCAS.

Forkner responded soon after: “Granted I suck at flying, but even this was egregious.”

The FAA plans to turn over more communications from Forkner to Congress later on Friday, sources said.

Boeing is revising the 737 Max software to add more safeguards and require the MCAS system to receive input from two key sensors.

The FAA reiterated that it is “following a thorough process, not a prescribed timeline, for returning the Boeing 737 Max to passenger service. The agency will lift the grounding order only after we have determined the aircraft is safe.”

Earlier this week, Southwest Airlines delayed the return of the plane to its flight schedule until February.