Obie Wilchcombe, a member of the Bahamas parliament and a family friend, told the Associated Press on Tuesday, "Everything was in place, the cremation was completed, and they decided to leave."
Funeral plans have yet to be announced.
In Ocala, Fla., where the Travoltas have a home, Mayor Randy Ewers said the city has sent the family condolences and would afford them time alone with their grief.
"They're fantastic people, really family oriented," Ewers said. "We want to respect their privacy as much as possible."
In a public statement Sunday, Travolta, 54, and Preston, 46, said of son Jett, 16, that they were "heartbroken that our time with him was so brief."
They also thanked "everyone who has sent their love and condolences."
Luyis Santana / Splash News Online
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