Vilma Soltesz, who weighed about 420 lbs (193kg), was refused a place on two flights in October.
She died of kidney failure before a suitable flight could be found, after refusing treatment from local doctors.
Delta Airlines said every effort was made to accommodate her but it had been “physically unable” to get her aboard.
But Peter Ronai, the lawyer acting for her husband, Janos Soltesz, told CBS: “They [the airlines] took on the responsibility to get her to Hungary, it’s their responsibility to get her back.”
Vilma Soltesz needed to return to New York from her holiday home in Hungary to resume medical treatment.
She suffered from kidney disease and diabetes and reportedly “did not trust” Hungarian doctors.
But the Dutch airline KLM was unable to get her on board a flight on which she had booked two seats to accommodate her.
Vilma Soltesz was then told to drive to Prague in the Czech Republic where she would be given seats on a larger Delta Airlines flight.
But, according to Peter Ronai, she was unable to be belted into that plane and “the captain came out of the cockpit and made her get off”.
Vilma Soltesz died of kidney failure before an alternative flight could be found.
In a statement Delta Airlines and KLM said they had done everything possible to assist the family.
“Our records indicate Delta staff in Prague made repeated attempts for nearly an hour to board the customer, but they were unable to get her onboard the aircraft,” Delta claimed.
Janos Soltesz is seeking $6 million (4.6 million euros) in damages from Delta and KLM.
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