Families of the victims of India’s deadliest aviation disaster in decades lined up at the main hospital in the western city of Ahmedabad early Friday, ready to offer DNA samples that could identify the bodies of loved ones they had seen off a day before.

The cruel but necessary exercise, which began hours after the crash of the Boeing 787-8 Dreamliner bound for London on Thursday afternoon, continued overnight as a clearer sense of the devastation began to emerge.

Prime Minister Narendra Modi of India arrived in Ahmedabad, which is the largest city of his home state of Gujarat, to survey the scene and visit those injured when the plane crashed into a building. In a sign of the alarm caused by the crash, India’s aviation regulators, in an order on Friday, directed Air India to carry out “additional maintenance actions” in its Boeing fleet “with immediate effect.”

Officials say that at least 269 people died in the crash of Flight AI171 and its aftermath, cautioning that the death toll could rise as emergency teams continue to comb through the site of the devastation. In addition to 241 passengers and crew, dozens perished as they were caught in the path of a plane that began descending on the dining hall of a college seconds after takeoff from a nearby airport, before exploding into flames on the ground.

Only one passenger survived and was being treated for his injuries, the airline and Indian officials have said. The details of how he survived are still patchy.

The plane was carrying 125,000 liters, or about 33,000 gallons, of fuel at the time of the crash, according to India’s home minister, Amit Shah. After returning to the ground, it skidded along, damaging buildings, before it burst into flames just about a mile southwest of Sardar Vallabhbhai Patel International Airport. The intense blast and flames made rescue impossible, he said, and left the bodies so badly damaged that DNA testing was needed for basic identification.

The city’s health services on Friday morning appeared overwhelmed by that task, as they hurried to carry out hundreds of DNA tests so they could hand over the bodies to mourning families growing restless at the hospital gates.

Dr. Vijay Shah, a medical official in Ahmedabad, said more than 250 bodies had been brought to Ahmedabad Civil hospital, less than a mile from the scene of the crash. By Friday afternoon, the hospital had collected DNA samples from over 200 people, officials said. The results were not expected until Saturday evening.

The hospital was struggling with the number of bodies.

By late afternoon on Friday, a strong stench was growing outside the facility, with volunteers handing out masks that made it bearable. Less than 10 bodies had been released to relatives after completion of identification and paperwork, according to multiple medical and police officials at the hospital. Ambulances were lining up to move some of the bodies for cold storage to other facilities.

Alkesh Patel, among those waiting outside the hospital building where the DNA testing was taking place, said his 70-year-old uncle, Neelkanth Patel, was among the passengers.

“He was my mother’s younger brother,” he said, as his distraught mother waited on a plastic chair next to him. “My mother is waiting to give the DNA sample.”

Just steps away, Salma Rafeek Memon, dressed in a traditional cotton salwar suit, sobbed on a bench. She had lost her nephew, killed in the plane crash along with his wife and two children. The young family had been visiting relatives in Mumbai and was connecting through Ahmedabad on their way back to London.

“This is their photo as they bid us goodbye from Mumbai,” Ms. Memon said, wiping away tears with the edge of her stole as she showed her cellphone displaying a picture of her nephew’s smiling family.

The Boeing 787-8 Dreamliner bound for London Gatwick Airport had taken off from the airport at 1:38 p.m. local time and shortly after crashed into the dining facility of a government medical college, where dozens of students were sitting for lunch. It also caused heavy damage to nearby apartment buildings where doctors and their families live.

Air accident investigators from Britain and the United States were expected to travel to India to support the investigation into the cause of disaster. On Friday, India’s civil aviation minister said that the plane’s flight data recorder, or black box, had been recovered.

Hari Kumar contributed reporting from New Delhi.