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A US passenger plane travelling from Seattle to Dallas was forced to turn back hours into its flight because a human heart had been left on board.

Southwest Airlines says the organ was flown to Seattle from California, where it was to be processed at a hospital to have a valve recovered for future use.

But it was never unloaded and its absence was not noticed until the plane was almost half-way to Dallas.

The heart itself had not been intended for a specific patient.

Details of the incident, which occurred on Sunday, were revealed in media reports on Thursday.

Passengers were said to have been shocked when the captain told them about the cargo and why the flight was turning back.

Some used their smartphones to investigate the length of time that a heart can be stored before it is no longer viable for a transplant operation - typically between four and six hours, according to experts.

The plane was reportedly in the air for about three hours.

A doctor who was among the passengers but not involved in the shipment of the organ, told the Seattle Times newspaper that the incident was a "horrific story of gross negligence".

Following the flight's return to Seattle, and was said to have been received within the required time frame, the newspaper added.

In a statement, Southwest Airlines said the heart reached its intended destination "within the window of time allotted by our cargo customer".

A spokeswoman for Sierra Donor Services, the nonprofit that organised the donation, said that the heart will now be processed so that its valves can be used for life-saving procedures, but added that these "won't be available for implant for quite some time".

Monica Johnson, Sierra Donor Services' executive director, said the donor's family had been notified of the travel delay.

"They are relieved their loved one's heart valves were received and will be able to help others," she said.

After the plane returned to Seattle it was taken out of service due to a mechanical issue that Southwest says was unrelated to the heart mishap.