A Southwest Airlines flight headed from Seattle to Dallas was turned back mid-flight after it was discovered that a human heart had been left on board, officials said.

The plane was over eastern Idaho, around 950km into the journey, when staff discovered the "life critical cargo shipment", which was meant for delivery back in a Seattle hospital after being transported from California.

BBC News reported that the heart was to be processed to have a valve recovered for future use, and that the heart itself has not been intended for a specific patient.

"Once we realised the error we immediately worked to return to Seattle," airline spokesman Dan Landson told AFP.

The airline did not provide the name of the company that shipped the organ, or confirm any further details.

But the Seattle Times reported that the flight's captain told passengers the cargo was a human heart.

The error is thought to have lost four hours - three hours in the air - and experts say a human heart can typically be stored for between four and six hours in cases of a transplant.