At least one person is known to have survived, police said, and the man told Indian media how he had heard a loud noise shortly after take-off.
The plane, a Boeing 787-8 Dreamliner, came down in a residential area, crashing onto a medical college hostel outside the airport during lunch hour. It was headed for Gatwick Airport, south of the British capital.
City police chief GS Malik told Reuters that 204 bodies had been recovered from the crash site - both passengers and medical students. Vidhi Chaudhary, another senior police officer, said police found one survivor and said there could be more.
"Thirty seconds after take-off, there was a loud noise and then the plane crashed," 40-year-old survivor Ramesh Viswashkumar told the Hindustan Times from his hospital bed, adding he was desperate to hear what had happened to his brother, who was also on the flight.
"It all happened so quickly. When I got up, there were bodies all around me. I was scared. I stood up and ran. There were pieces of the plane all around me.
"Someone grabbed hold of me and put me in an ambulance and brought me to the hospital."
Police chief Malik said the bodies recovered could include both passengers and people killed on the ground.
"Chances are there could be some more survivors among those who are in hospital," police officer Chaudhary told Reuters.
"There are also chances that the death toll will go up. More than 50 injured are in hospitals at present."
Parts of the plane's body were scattered around the building into which it crashed. The tail of the plane was stuck on top of the building.
The passengers included 217 adults, 11 children and two infants, a source told Reuters. Of them, 169 were Indian nationals, 53 were Britons, seven Portuguese, and one Canadian, Air India said.
Australia's High Commission in New Delhi and the Consulate-General in Mumbai are urgently following up with the local authorities to find out whether any Australians were on board, a spokesperson for Australia's Department of Foreign Affairs said.
According to air traffic control at Ahmedabad Airport, the aircraft departed at 1.39pm local time from runway 23. It gave a Mayday call, signalling an emergency, but thereafter there was no response from the aircraft.
One television channel showed the plane taking off over a residential area and then disappearing from the screen before a huge jet of fire can be seen rising into the sky from beyond the houses.
Boeing said it was aware of initial reports and was working to gather more information. Boeing shares fell five per cent as the crash posed a major setback for the plane manufacturer as its new CEO looks to rebuild trust following a series of safety and production challenges.
"The tragedy in Ahmedabad has stunned and saddened us," Indian Prime Minister Narendra Modi posted on X.
"It is heartbreaking beyond words."
British Prime Minister Keir Starmer said images emerging of the crash were "devastating", and that he was being kept informed as the situation developed. A Buckingham Palace spokesperson said King Charles was also being kept updated.
The owners of Air India have said it will provide 10 million rupees ($A179,000) to the families of each of the dead, cover all medical expenses of those injured and help rebuild the hostel of the medical college.
