The Los Angeles Times, citing unnamed emergency officials, said Fisher, 60, was in critical condition after she was stricken by a "cardiac episode" on the trans-Atlantic flight, which landed at Los Angeles International Airport.
According to the celebrity news website TMZ.com, Fisher suffered a "massive heart attack" 15 minutes before landing and an emergency medical technician who was aboard was ushered to the first-class cabin to aid the actress-writer.
No representatives for the performer were immediately available to comment. The city Fire Department confirmed that its emergency personnel met an arriving flight at the airport to treat a patient in "cardiac arrest," but declined to identify the individual, citing medical confidentiality laws.
However, two passengers who said they were aboard the flight and sitting near Fisher posted messages on Twitter reporting that she had fallen ill.
Well-known YouTube performer Anna Akana tweeted that Fisher had "stopped breathing," and comedian Brad Cage, who said he and Akana were sitting in front of the actress, tweeted separately that Fisher was taken off the plane by paramedics.
United Airlines issued a statement saying that Flight 935 from London to Los Angeles was met on the ground by medical personnel after the crew reported that a passenger was "unresponsive." The airline also declined to name the passenger.
Fisher, who has been on a tour promoting a new memoir, "The Princess Diarist," is best known for her role as the intrepid Princess Leia in several of the "Star Wars" movies.
She made headlines in November with the disclosure to People magazine that she carried on a three-month love affair with her "Star Wars" co-star, actor Harrison Ford, who played the swashbuckling pilot Han Solo, during the making of the first film in the series in 1976.
She reprised her Princess Leia role in two sequels and returned last year in Disney's reboot of the franchise, "The Force Awakens," appearing as the more matronly General Leia Organa, leader of the Resistance movement fighting the evil First Order.
Fisher, the daughter of actress Debbie Reynolds and singer Eddie Fisher, made her show business debut at age of 12 in her mother's Las Vegas nightclub act. But her adult career was dogged by substance abuse and mental health issues.
She entered a drug treatment center in the mid-1980s to battle addiction to cocaine and later wrote the bestselling novel, "Postcards From the Edge," based on her experience. The book was adapted into a 1990 movie starring Meryl Streep. Fisher also acknowledged being briefly hospitalized in 2013 due to bipolar disorder.
Fire Department spokesman Erik Scott said city paramedics met an arriving flight at the airport shortly after noon (2000 GMT) for "a patient on an inbound flight in cardiac arrest." He said rescue personnel "provided immediate advanced life support and aggressively treated and transported the patient to a local hospital."
The Los Angeles Times account cited one unnamed source as saying the actress had been "in a lot of distress on the flight."
NBC News, also citing unnamed sources, said she had suffered a full cardiac arrest on the flight and that her condition was "not good."
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