David Paul, 37, and his wife, Michelle Paul, 35, died two days apart after checking into their hotel May 22 on Denarau Island.
The Fort Worth couple contacted relatives, saying that they'd begun feeling unwell two days into their holiday.
"We are both going to doctor now," Michelle texted her parents. "We have been throwing up for 8 hours. Dave has diarrhea. My hands are numb. We will text when we can."
They received anti-nausea medication and fluids, but their health became worse. Michelle died on May 27, and her husband died two days later.
Fiji officials no longer believe the couple died from an infectious disease.
"Investigations by the Ministry and other partners, which included post-mortem examination, laboratory investigations to exclude a wide range of viral and bacterial causes, toxicology and microscopic examination of tissues, have identified no infectious causative agent," the Ministry of Health and Medical Services said, according to news station DFW-TV.
The ministry has been working with the US Centres for Disease Control (CDC) and Prevention and the World Health Organisation to determine the cause of death.
The couple's remains are still on the island as the CDC concentrates on a toxicology investigation, news station KTNV reported.
Michelle's father Marc Calanog told the Star-Telegram he was "stunned" when he was told of the tragedy.
The couple left two children - David's daughter from a previous marriage and an adopted 2-year-old boy.
