(CNN) Sen. John Kennedy is calling out United Airlines, demanding an "immediate explanation" of the death of a dog on a flight this week, and saying other animals have suffered while in United's care.

"For many people, pets are members of the family," Kennedy writes in a letter sent today to the president of United Airlines, J. Scott Kirby. "They should not be treated like insignificant cargo. Frankly, they shouldn't be placed in the cargo hold much less an overhead bin."

The Louisiana Republican's letter was prompted by the death of a French bulldog that has captured national attention this week. On Monday, on a flight from Houston to New York, the dog's owners were told to put their pet inside an overhead bin. After the three-hour flight the dog had died.

Kennedy tweeted that he will file a bill Thursday to prohibit airlines from putting animals in overhead bins.

"I will be filing a bill tomorrow that will prohibit airlines from putting animals in overhead bins. Violators will face significant fines. Pets are family," Kennedy wrote on Twitter.

Read More