A dog has died on a United Airlines plane in the United States after a flight attendant ordered its owner to put the pet in the aircraft’s overhead locker.

United said it took full responsibility for the incident on the Houston to New York flight on Monday night local time.

In a statement, United described the death “a tragic accident”.

“We assume full responsibility for this tragedy and express our deepest condolences to the family and are committed to supporting them,” the US airline said in a statement.

“We are thoroughly investigating what occurred to prevent this from ever happening again. Pets should never be placed in the overhead bin,” the statement added.

The dog, a French bulldog, was in a small pet carrier designed to fit under an airline seat.

Passengers reported that they heard barking during the flight and didn’t know that the dog had died until the plane landed at New York’s LaGuardia Airport.

Fellow passenger Maggie Gremminger told the One Mile at a Time travel website she was sitting behind the woman with the dog at the time of the dispute.

“I witnessed a United flight attendant instruct a woman to put her dog carrier with live dog in an overhead bin,” she was quoted as saying.

“The passenger adamantly pushed back, sharing verbally that her dog was in the bag. The flight attendant continued to ask the passenger to do it, and she eventually complied.

“By the end of the flight, the dog was dead. The woman was crying in the airplane aisle on the floor.”

Ms Gremminger also posted a photo on Twitter of a woman she said was the dog’s owner.

I want to help this woman and her daughter. They lost their dog because of an @united flight attendant. My heart is broken. pic.twitter.com/mjXYAhxsAq

— Maggie Gremminger (she/her) (@MaggieGrem) March 13, 2018

Other passengers posted pictures on social media purported to be of the dog in its carrier after it was found dead.

United spokesman Charles Hobart said the flight attendant told the dog’s owner to put the pet carrier in the overhead locker because the bag was partly obstructing the aisle. It is unclear why the carrier was not placed under a seat, he said.

Mr Hobart said United is investigating the incident and talking to the flight attendant, whom he declined to identify.

He said the airline refunded the tickets purchased for the dog owner and her two children and the fee that they paid to bring a pet on board – typically $US200 ($254).

The cause of the dog’s death was not immediately known. Mr Hobart said United offered to pay for a necropsy.

Last year, 18 animals died while being transported on United – there were six cases on all other US carriers combined, according to the Department of Transportation.

The dog’s death comes after a group of US businessmen last year sued United Airlines over the death of a giant rabbit during a flight from London to Chicago.

The 10-month-old rabbit, named Simon, was found dead on April 20, 2017 and then cremated by the airline.

The three businessmen bought Simon from a UK breeder with the intention of showing him at the Iowa State Fair, and then displaying him and selling related merchandise to raise money for the annual event.

Simon, reportedly measured 1.04 metres long, was the offspring of Darius – who holds the Guinness World Record for longest rabbit.

The lawsuit alleged United has a poor record of transporting animals, stating the airline accounted for a third of all animal deaths via US air travel in the past five years.