The Santa Monica Fire Department responded to the scene around 4:25 p.m., and firefighters saw the aircraft engulfed in flames after the crash.
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Officials say the plane took off around 3:30 p.m. for an introductory flight lesson along the coast of Malibu. The plane was cleared for landing when the student and instructor were returning to the airport.
"The airplane shortly after or possibly just before touch down, pitched into the air aggressively -- nose up, climbed to about a hundred feet and then rolled to the ground, where it impacted the ground," said Eliott Simpson, an investigator with the National Transportation Safety Board.
Firefighters extinguished the flames within minutes. Footage from the scene showed the burned wreckage of the aircraft on the tarmac.
The Federal Aviation Administration identified the aircraft as a two-seat, single-engine Piper Sport plane. The Santa Monica Fire Department said the plane was operated by a flight school, later identified as the Santa Monica Flyers.
Officials with the NTSB confirmed the victims killed were an instructor and a student.
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They were pronounced dead at the scene. Their names were not immediately released.
According to the NTSB, witnesses and surveillance video saw the plane's final moments in the air.
The Santa Monica Fire Department said neighborhoods nearby were not impacted by the crash.
The NTSB is in charge of the investigation. The airport was closed for the probe but is expected to reopen Friday.
The crash comes as the city prepares to shut down the airport by the end of 2028.
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Lawsuits and environmental safety concerns from neighbors and high-profile publicity have plagued the airport in recent years.
In 2015, actor Harrison Ford crashed on a Venice golf course and alerted air traffic control right before going down that he had to return to Santa Monica Airport because of engine failure.
A GoFundMe has been set up by the family of the student pilot who tragically lost his life.