Chief executive Simon Thompson has been asked to clarify his statements to the Business, Energy and Industrial Strategy committee last week.
MPs said they were sent hundreds of complaints regarding his claims that came amid a dispute with the Communication Workers Union.
In a letter to him, committee chairman Darren Jones said: “Contrary to your evidence, we have been told that managers in many delivery offices are advising workers that parcels are still to be prioritised.”
The MPs also have “concerns” about how Royal Mail handles sick pay, he said.
Mr Jones added: “We’ve had significant quantities of evidence that suggest his answers may not have been wholly correct.”
Royal Mail said it welcomed the chance “to expand on any points on which the committee would like clarification”.