runway at Bajpe airport on Saturday and ploughed into a forested gorge, bursting into flames.
Some of the eight people who survived the crash told how they had escaped death as the fuselage broke into pieces and filled with fire and thick choking smoke.
"A big team of experts has arrived for the operation," airport director P.K. Thomas told AFP at the scene of the disaster, about 20 kilometre (12 miles) from the southwest coastal city of Mangalore.
Officials from the Directorate General of Civil Aviation (DGCA) said the "black box" digital data recorder that should shed light on the cause of the disaster had not yet been found.
"We should certainly get it today," a DGCA source said on condition he was not named, adding they were also still searching for the cockpit voice recorder.
The probe into the crash resumed at first light on Sunday with the wreckage area cordoned off. Immediately after the accident, crowds of local residents had streamed to the site to help rescue victims.
About 25 investigators used mechanical metal-cutters to start their examination of the plane's remains, while hired labourers cleaned up debris scattered widely across the muddy slopes.
"All 158 bodies have been recovered but only 72 have been identified," rescue coordinator Yogendra Tripathi told AFP on Sunday morning. "We will carry out DNA tests on the remaining bodies beginning today."
The few survivors of India's worst aviation disaster in 14 years described hearing a loud thud shortly after touchdown.
Officials said the landing conditions were fair with good visibility and reported there had been no distress call from the cockpit.
Civil Aviation Minister Praful Patel, who flew to the crash site, said eight passengers had survived.
It was the country's deadliest crash since 1996 when two passenger planes collided in mid-air near New Delhi with the loss of all 349 on board both flights.
One survivor, Umer Farooq, spoke to reporters from his hospital bed where he was being treated for burns to his arms, legs and face.
"The plane veered off toward some trees on the side and then the cabin filled with smoke," he said. "I got caught in some cables but managed to scramble out."
Television images from the immediate aftermath of the crash showed smoke billowing from the fuselage as emergency crews, who struggled down steep, wooded slopes to reach the aircraft, sought to douse the fire with foam.
"The preliminary observation is that the aircraft touched down and did not contain itself within the runway space," minister Patel said.
He described the chief pilot, a Serbian national, as a "very experienced" flier who had logged 10,000 hours of flying time.
Stressing that it was too early to determine the precise cause of the crash, Patel noted that the sanded safety area surrounding the runway in the event of an overshoot was shorter than at some airports.
"It does not have much of a spillover area and in this case apparently it had not been able to stop the plane," he said.
Air India Express is a budget airline operated as a subsidiary by the state-run carrier. Many of the passengers were Indian migrant workers returning from jobs in the Gulf to visit their families.
US-based aircraft manufacturer Boeing said it was sending a team of investigators to India to help in the inquiry.
The last major plane crash in India was in 2000, when 61 people were killed after a passenger jet plunged into a residential area near the eastern city of Patna.
The country's air safety record has been good in recent years despite the rapid increase in airlines keen to serve increasingly wealthy domestic customers.
Saturday's disaster came as Air India is struggling to turn round its finances after posting a net loss of more than one billion dollars last year.