The family is too poor to pay the bill, Inter-Asian News Service reported.
Speaking of his twins, Saba and Farah, father Shakeel Ahmad, said the girls "share everything, their pain and happiness. The Supreme Court order has given us fresh hope."
Saba, lying on a bed with Farah at their home in Patna, said the court "has brought us a ray of hope," and Farah, smiling, agreed.
Ahmad, who runs a small roadside eatery, said the girls' condition has been worsening.
"Both girls are not keeping well for the last two years," he said. "Their condition is deteriorating. We are poor and helpless. We can only pray to God."
The girls' mother, Rubina Khatoon, said they eat very little food and often cry in pain.
A ruler in the Gulf region had promised to pay for the operation a few years ago, Ahmad said. But the father said after initial consultation at Delhi's Apollo hospital, "everything was forgotten."
The twin girls have distinct brains and are neurologically and psychologically normal but only one of them has kidneys.