An Indian-origin woman has died while her daughter and the pilot instructor were injured in a small plane crash in the New York area when they were on a "demonstration flight", media reports said.

Roma Gupta, 63, and her daughter Reeva Gupta, 33, were on board the small plane on Sunday as its pilot reported smoke in the cockpit before crashing near Long Island homes, NBC New York TV channel reported.

Roma was killed when the four-seater single-engine Piper Cherokee plane went down in flames as it was returning to the Republic Airport on Long Island from where it had also taken off.

Her daughter Reeva and the 23-year-old pilot instructor are in hospital with severe burns, according to the report.

"The two patients critically injured, severely burned, to my knowledge they were pulled from the plane from a civilian," North Lindenhurst Fire Dept. Chief Kenny Stallone said.

Roma died in the crash. Her daughter, Reeva, is in critical condition at Stony Brook Hospital with third-degree burns. Reeva is a physician's assistant in the Mount Sinai system, whose colleagues say she has a long, painful recovery ahead.

The flight instructor operating the plane was also in critical condition Monday, according to the Danny Waizman Flight School, which owns the plane.

Oleh Dekaylo, the attorney for Danny Waizman Flight School said the pilot had all his ratings and certifications, and the plane involved in the crash had just passed two stringent inspections, the most recently last week.

"It was a demonstration flight, an introductory flight to see if people are interested" in flying lessons, Dekajlo, the lawyer for Danny Waizman Flight School, told the channel.

Suffolk County police say the pilot was on a tourist flight. The flight path shows the plane went over the South Shore beaches. Then the pilot reported smoke in the cabin, which he radioed into Republic Airport air traffic controllers, the News12 New Jersey website reported.

The attorney for the plane's owner said that the plane had gone through numerous inspections, including one just recently.

The National Transportation Safety Board will continue the investigation to determine the cause of the crash. The Federal Aviation Administration is also investigating the crash.

Federal investigators are expected to return to the crash site for a third time on Tuesday to remove the wreckage for further analysis.

Meanwhile, a GoFundMe created for the Gupta family has raised more than USD 60,000.

Except for the headline, this story has not been edited by The Telegraph Online staff and has been published from a syndicated feed.