Harbourgh MP Edward Garnier said in the House of Commons that a freight flight from Nottingham East Midlands Airport overshot the runway on 4 February.
He called for an investigation into reports the plane was then forced to fly low over nearby villages.
Airport officials have denied there was a near-miss but agreed to refer the claims to the CAA.
No skid marks
An airport spokesman said: "Nottingham East Midlands Airport can confirm that, following an internal investigation, no evidence of a breach of safety was found, therefore, no Mandatory Occurrence Report was required.
"The aircraft did not overshoot the runway as claimed and left no marks on the grass at the end of the runway as claimed.
"Any incident which causes a safety alert would be immediately reported to the Civil Aviation Authority, but even though this was not necessary in this case, in view of the public concern, we have asked the CAA to investigate the matter".
The Deputy Speaker of the House of Commons, Sir Michael Lord, called on ministers to respond to Mr Garnier's request.
Mr Garnier said the flight records for the aircraft were due to be deleted and he urged ministers to intervene.
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