(CNN) -- Actors John Travolta and Kelly Preston said Sunday they are "heartbroken" over last week's death of their teenage son.
Jett Travolta, 16, died Friday after a seizure while vacationing with his family in the Bahamas, an attorney for the family has said.
Jett Travolta, right, joined his father weeks ago in Paris, where John Travolta has been filming a movie.
"Jett was the most wonderful son that two parents could ever ask for and lit up the lives of everyone he encountered," Jett Travolta's parents said in a statement Sunday.
"We are heartbroken that our time with him was so brief. We will cherish the time we had with him for the rest of our lives."
An autopsy on Jett Travolta will be performed Monday, family attorney Michael Ossi said last week.
The boy hit his head after the seizure, but the exact cause of death is not known, Ossi said Friday.
His body will be transferred to Ocala, Florida, for burial, Ossi said. Watch John Travolta and son, Jett, in Paris »
The Travoltas also have a daughter, Ella, 8.
In Sunday's statement, Preston and John Travolta extended their "deepest and most heartfelt thanks to everyone who has sent their love and condolences."
"We have received many messages of condolence from around the world and we want to thank everyone for their prayers and support," the statement read. "It has meant so much to us. It is a beautiful reminder of the inherent goodness in the human spirit that gives us hope for a brighter future."
Bahamian police on Friday said a caretaker at the West End resort where the Travoltas were vacationing found the teenager unconscious in the bathroom. Jett Travolta was taken by ambulance to Rand Memorial Hospital in Freeport and was pronounced dead on arrival, police said. iReport.com: Can you relate to the loss of a child? Share your story
Obie Wilchcomb, a former Bahamian minister of tourism, told CNN's "Larry King Live" on Friday the family was on the island for a gathering of 60 family and friends who were arriving throughout the day as the tragedy unfolded. See photos of Jett with his family »
Jett Travolta had a developmental disability that his parents have linked to Kawasaki disease, an inflammatory disorder of the artery walls that most commonly occurs in young children and can lead to heart disease. Watch CNN's Sunjay Gupta discuss Kawasaki disease »
In 2001, John Travolta told CNN's Larry King that his son had a near brush with death related to the condition.
"I was obsessive about cleaning -- his space being clean, so we constantly had the carpets cleaned. And I think, between him, the fumes and walking around, maybe picking up pieces or something, he got what is rarely a thing to deal with, but it's Kawasaki syndrome," Travolta said of his then-2-year-old son. Watch Travolta talk about his son's condition »
"It was that the immune system overreacts, because they have almost the equivalent of metallic chemical," Travolta said.
In 2003, Kelly Preston told Montel Williams that when Jett was 2, he became ill with flu symptoms, including fever, rashes and swollen lymph nodes, before a doctor diagnosed him with Kawasaki disease.
Echoing her husband's comments, Preston blamed chemicals in household cleaners and pesticides for attacking her son's immune system, triggering the condition.
A dedicated Scientologist, Preston told Williams that she credited a detoxification program from the writings of Scientology founder L. Ron Hubbard with helping improve her son's health.
Kawasaki disease is characterized by fevers and inflammation in the blood vessels that can be caused by a number of inciting factors, including virus, bacteria or infection, CNN's Dr. Sanjay Gupta said on "Larry King Live."
"You get pretty sick for a few days. In the worst-case scenario, sometimes it can affect the blood vessels of the heart, called the coronary arteries," Gupta said. "Sometimes they can develop aneurysms in it. That's probably the most dangerous thing. But again, this is typically a disease associated with young children. It's typically in Japan, and it's pretty rare."
Gupta said it was rare for teens to display symptoms of the disease.
"Most of the patients are usually between 2 and 5 years old. Sometimes they get up to age 8. But it's very rare in fact for someone to be in their teens and still have symptoms of Kawasaki. They may have had it earlier in life, but to still have any manifestations of it is unusual," he said.
The causes of Kawasaki disease are unknown. Some scientists think it's caused by an infectious agent, such as a virus. Some studies have noted a link between the disease and carpet cleaning chemicals.
John Travolta gained fame in the 1970s, starring in the television series "Welcome Back, Kotter" and the movies "Saturday Night Fever" and "Grease." His career got a boost in 1994 with his second Best Actor Oscar nomination, for his role as a hit man in "Pulp Fiction."
Preston has numerous TV and movie credits, including a supporting role in 1996's "Jerry Maguire."
CNN's Valerie Streit contributed to this report.
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