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

Roma Gupta, 63, was killed on Sunday on Long Island when the plane, a four-seater single-engine Piper Cherokee, 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 Gupta, 33, and the pilot are in hospital with severe burns, according to NBC New York TV channel.

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

The crash in a residential area of Lindenhurst that missed houses and crashed in a field was captured on home surveillance cameras.

A witness told CBS New York TV, "The pilot did a great job, in my opinion, trying to avoid any houses, people, and traffic."

Reeva Gupta is a neurosurgery physician's assistant with the Mount Sinai Hospital System, according to an appeal set up by co-workers on Gofundme.

"To help fulfill a long-standing wish of theirs, they booked a flight lesson", according to the appeal which had collected nearly $70,000 by Tuesday evening to help Reeva Gupta and her family".

It said that she is "fighting for her life" with third-degree burns all over her body.

WABC TV reported that the 23-year-old pilot is a certified flight instructor who issued a "May Day" call - the aviation distress signal - that there was smoke in the plane before it went down. (KB/IANS)