Authorities have launched an inquiry into the causes of the oxygen disruption but denied reports that it had caused the deaths at the Baba Raghav Das Hospital in Gorakhpur, Uttar Pradesh state.
Indian media said 30 children died on Thursday and Friday because of the lack of oxygen on wards. Suppliers' bills had allegedly not been paid.
"Sixty patients have died at the hospital in the last five days but we don't think it's linked to reports of oxygen shortage," Anil Kumar, Gorakhpur's divisional commissioner told AFP.
State health minister Sidharth Nath Singh announced later that four more deaths had been reported Saturday, taking the toll to 64 over the six days starting Monday.
Ingh denied that any of the deaths were linked to the oxygen shortage.
Twenty-three children died on Thursday, when, according to a statement shared by the office of state chief minister, "the pressure of the liquid oxygen supply became low and 52 reserve oxygen cylinders were pressed into service".
The office of Prime Minister Narendra Modi said on Twitter that Modi was "monitoring the situation in Gorakhpur" and was in touch with state authorities. Modi's conservative nationalist party controls the state.