The baby, who was born yesterday morning, was first rushed to Sanjay Gandhi Memorial Hospital (SGMH) and then later taken to Dr Baba Saheb Ambedkar Hospital, where he was declared "brought dead" by doctors.
The baby, was born at home to Manoj, 27, and Tulsi, 22, after seven months of her pregnancy, doctors said.
"Our baby was delivered at home by a midwife, who then alerted us that he was having some breathing problems, and told us to take him to the nearest hospital. So, we rushed the baby to SGMH," Manoj said.
"But, doctors, there (at SGMH) said, the hospital did not have the oxygen facilities needed for the child and referred us to Dr Baba Saheb Ambedkar Hospital, where we then rushed to, but in vain," he alleged.
The SGMH authorities, however, denied the allegation, claiming, "the parents left the hospital on their own, without informing anyone".
"The baby was brought to the pediatric casualty department and he was initially attended to by junior and senior resident doctors," SGMH Medical Superintendent PS Nayyer told PTI.
A senior pediatrician was later attending to him, when another child developed a seizure, and so he had to go and attend to the other child, Mr Nayyer said.
"Meanwhile, the parents of the baby left without informing any staff at the hospital," he claimed.
The distance between SGMH and Baba Saheb Ambedkar Hospital, that are both northwest Delhi, is about 4-5 km. They travelled in an e-rickshaw to Baba Saheb Ambedkar Hospital from SGMH and took about one hour because of traffic.
The couple's first child, a three-and-a-half- year-old boy, was also born at SGMH.
The death was the second such fatality within a week in Delhi as last Thursday a newborn girl had died also allegedly due to lack of critical care facilities.
The death of the newborn yesterday also comes just days after Delhi Chief Minister Arvind Kejriwal had directed Health Minister Satyendar Jain to come up with a "concrete action plan" within a week on providing life support system for critical patients in the city's government hospitals.
Mr Nayyer said after the incident an inquiry panel was set up and the panel submitted its report in the evening.
"According to the report, child was born premature (of seven-month-pregnancy) at home. He did not show any respiratory distress and so was not put on a ventilator. We have one ventilator in child casualty department, and it was unused when the baby was brought to SGMH," Mr Nayyer said.
"We have seven oxygen supply units at the hospital and so, the reason he was not put on a ventilator, was because, it was not recommended by doctors, and not because we lacked it," he claimed.
Ventilator is a machine designed to facilitate breathing for a patient who is physically unable to breathe, or breathing insufficiently.
A senior doctor said babies born of seven-month pregnancies can survive as long as they weigh at least 500 gm.
Ashok Aggarwal, an advocate and member of the Delhi High Court-constituted EWS Patients Monitoring Committee, expressed his shock over the incident and blamed the hospital.
"When a baby was in need of medical care, the doctor went to attend to another baby. Was there no other doctor? This newborn should have been properly attended and which the SGMH authorities did not," he alleged.
According to a statement released by the Delhi government earlier this week, the primary objective of the concrete action plan sought by Mr Kejriwal was to ensure that the "live data" of functional critical care facilities in all Delhi government hospitals is readily and easily available in the first place.
It has been noticed in a number of cases that family members or relatives or friends of patients in critical condition, who rush them to hospitals, are turned away, citing the common excuses of either lack of facilities or non- availability of beds, the Delhi government had said.