A dog has died during a United Airlines flight after a flight attendant insisted it be placed in an overhead bin.

The black French bulldog was in a pet carrier during the flight from Houston to New York on Monday.

United Airlines said it took responsibility for the death, saying pets should not be placed in the overhead storage compartments.

"This was a tragic accident that should never have occurred," the airline said in a statement, adding that it expressed its "deepest condolences to the family".

Passenger Maggie Gremminger, 30, who was seated behind the pet owner, said the owner was told to put her dog in the compartment after boarding with two kids including an infant, according to The New York Times.

"The pet owner was very adamant that she did not want to put the pet carrier up above," Ms Gremminger said, according to the Times.

"She was saying, 'My dog is in here, no, this is my dog.' The flight attendant, in response, really just continued to ask her to put it above because it was a hazard where it was, it was a safety emergency, someone could trip."

This was the latest in a string of PR nightmares for United Airlines.

Last year, a man was dragged kicking and screaming from an overbooked plane in Chicago, and mobile phone footage of the incident went viral.