The US Department of Transportation said on Wednesday it was examining the events that led to the French bulldog's death.
US Senator John Kennedy, who earlier sent a letter to United Airlines President Scott Kirby demanding information on the high number of animals that have died in the carrier's care, wrote on Twitter that he planned to file a bill on Thursday that would prohibit airlines from putting animals in overhead bins.
"Violators will face significant fines. Pets are family," he wrote.
Kennedy, in his letter, said United's "pattern of animal deaths and injuries is simply inexcusable."
He cited figures from the Transportation Department that of the 24 animals that died on US carriers last year, 18 were on United flights.
The actions came after a United flight attendant insisted that the bulldog's owner, Catalina Robledo, put her pet, which was in a dog carrier case, in an overhead storage bin during a 3-1/2-hour flight from Houston to New York on Monday.
The family told CBS they heard the puppy, named Kokito, barking for two hours during the flight before he went silent. The family said they were unable to check on the dog because of turbulence that forced them to stay seated.
The Department of Transportation "is looking into the circumstances surrounding the recent death of a pet onboard a United Airlines flight," an agency spokesman said on Wednesday.
The Federal Aviation Administration is also looking into the incident and will "review the airline's investigation," FAA spokesman Greg Martin said.
United said that by next month, it would issue brightly coloured bag tags to passengers travelling with in-cabin pets to help flight attendants easily identify the animals.