New York police on Friday said they had no evidence indicating that two sisters whose bodies were found duct-taped together in Manhattan had been killed.
"There is nothing pointing to a crime as of yet," said a New York Police Department spokesman, adding that "it is still very much a live investigation" without providing details of any probable cause of death.
The two young women, identified as Rotana Farea, 22, and her sister Tala, 16, were found on the banks of the Hudson River last week with no visible signs of trauma, dressed all in black, with fur-trimmed coat collars, and bound together at the ankles and waist by duct tape.
It has since emerged that the sisters were Saudi nationals, and had run away several times from their family's home in Virginia where they had not lived since the end of 2017.
They had been placed in a shelter but left Fairfax County in August and set out for New York.
They stayed in several different upscale hotels in the city and maxed out a credit card, according to a NYPD spokesman quoted by US media.
A witness reportedly saw the two girls early on October 24 on a playground near the Hudson, where they appeared to be praying.
Police said the two sisters were alive when they entered the river that separates New York from New Jersey.
Suicide is among the hypotheses as to the cause of their deaths.
Another rumour raised in the mysterious case alleges that the Saudi embassy threatened the two sisters or their family with repatriation for seeking asylum in the United States, and that they were afraid.
A police official appeared to confirm Friday that the two girls had indeed applied for asylum, but did not provide further detail.
Fatimah Baeshen, spokeswoman for Saudi Arabia's US embassy in Washington, tweeted that "Reports that we ordered anyone related to the Saudi sisters, Tala and Rotana Farea, God rest their souls, (who recently died tragically in NY), to leave the US for seeking asylum; are absolutely false."
"Details are still under investigation and will be shared in due course," she said.