The couple was taken to a local hospital with severe symptoms, where they died several days later and days apart, according to "Today."
Michelle's father, Marc Calanog, told "Today" that his daughter contacted him one day before they were about to come home to say she and her husband got sick and were going to a local clinic.
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The exact cause of death is still not known, but WFAA reported that island authorities confirmed an illness is a factor, according to the Fiji Broadcasting Corporation.
"Nobody's telling me what was the cause of the death, and that's very hard for me," Marc Calanog told "Today."
Marc Calanog said the couple’s bodies will not be returned until a cause of death is determined. If the cause is found to be an infectious disease, their bodies will be cremated.
Local authorities in Fiji are investigating, ABC News reported.
"We are closely monitoring local authorities' investigation into the cause of death," a spokesperson for the U.S. State Department said in a statement to NBC News. "We stand ready to provide all appropriate consular assistance."