NEW YORK (Reuters) - New York police were still trying to piece together on Wednesday a mystery over two young women whose bodies were discovered a week ago on the rocky Manhattan shore of the Hudson River, bound together with duct tape around their waists and ankles.

Since then, New York City police have determined that Tala Farea, 16, and Rotana Farea, 22, were sisters from Saudi Arabia living in Virginia, and at least one of them was reported missing two months ago.

The city’s medical examiner has yet to determine the cause of death, be it a double homicide or a suicide pact. The medical examiner’s office said the bodies were not decomposed when found by a passer-by on the afternoon of Oct. 24, indicating they had not been dead long.

The sisters had recently requested asylum in the United States without giving a reason for the application, the New York Times reported, citing police. The sisters’ mother also received a call from the Saudi Arabian embassy in Washington telling her about the asylum applications, the Times reported.

The New York Police Department declined to confirm the Times’ report. The sisters’ family could not immediately be reached for comment.

Saudi Arabia’s consulate general in New York did not comment on the Times report directly.

In a statement, the consulate said it had appointed a lawyer to follow the case “to avoid inaccurate reporting.” The Saudi embassy in Washington was also extending its “support and aid in this trying time” to the sisters’ family, the statement said.

The two sisters were students accompanying their brother in Washington, the consulate general said. Rotana Farea had been enrolled at George Mason University in Fairfax, Virginia, but left in the spring and may have moved to New York at some point, according to media reports.

New York detectives have been sent to Fairfax to look into the sisters’ movements there. The police department released new passport-style photographs on Wednesday showing the two young women with headscarfs over their hair.

“Are there any clues down in Virginia in their past life?” Dermot Shea, the New York Police Department’s chief of detectives, said to reporters this week. “We’re out to get justice for those two girls.”