The parents of a teenage girl run over and killed by emergency vehicles after the Asiana Airlines crash landing at San Francisco airport is suing the city, saying rescuers were reckless and poorly trained.

The parents of Ye Meng Yuan, 16, have filed a wrongful-death action, claiming firefighters and police responding to the crash failed on multiple fronts to properly rescue the girl, the San Francisco Chronicle said.

Ye was planning to visit Google and Stanford University with her friend, Wang Lin Jia, 16, before travelling to Southern California to attend a Christian summer camp.

Both girls were sitting in near the rear of Asiana Flight 214 on July 2 last year when the plane clipped a seawall on approach, snapping off the tail. Wang also died along with another young Chinese passenger, Liu Yi Peng, 15.

Ye was laying on the ground near the wreckage when she was run over by two vehicles. The San Mateo County coroner concluded that the vehicles killed her.

The lawsuit by her parents, Gan Ye and Xiao Yun Zheng, who live in China, says Ye was "lying helpless on the ground" after the crash, but rescue workers "inexplicably, failed to evaluate her condition, treat her, mark her location, or remove her from the perilous location where she lay curled in the 'foetal position'."

The lawsuit, filed in San Mateo County Superior Court, seeks unspecified damages.

San Francisco city attorney spokesman Gabriel Zitrin declined to comment.