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By Jonathan Dienst and Dareh Gregorian

The two Saudi sisters whose bodies were found bound together in New York's Hudson River were running out of money and were desperate not to return home, investigators said Friday.

In a briefing at police headquarters in Lower Manhattan, NYPD Chief of Detectives Dermot Shea shed new light on the sisters' mysterious disappearance — and their macabre deaths, which law-enforcement sources have previously told NBC News appeared to be suicide.

"This is a tragedy all the way around," Shea told reporters Friday, adding that there's "no credible information that a crime has taken place."

The sisters, Rotana Farea, 23, and Tala Farea, 16, were initially reported to have disappeared from their mother's Fairfax home on Aug. 24 — two months to the day before their fully-clothed bodies washed up on rocks on the Upper West Side of Manhattan, bound together by duct tape at their waists and feet and facing one another.

The timeline revealed Friday differed from earlier reports. Shea revealed that neither sister had lived with their parents since Nov. 30, 2017, when they ran away.

He said there were abuse allegations involving other family members, which were not corroborated. But the pair were removed from the home, and placed in a "shelter-type" facility in Virginia similar to one for domestic violence victims, he said.

They remained there until Aug. 23 or 24, when they vanished.

Police have been able to largely retrace their steps through detective work, but still "do have some gaps to fill," Shea said.

The older sister's credit card records show they headed to Washington, D.C., after leaving Fairfax, and then made their way to Philadelphia. They arrived in New York on Sept. 1 — 11 days before they were reported missing.

Shea said the sisters stayed at a number of "high-end hotels" in Manhattan, and used the credit card to go shopping and order their meals together.

Detectives are also investigating claims they applied for asylum to remain in the United States. Detectives were told the sisters had previously made statements "they would rather inflict harm on themselves, commit suicide, than return to Saudi Arabia," Shea said.

Deportation was "a fear of theirs," he added.

In video police have been able to obtain of the pair from about a week before their deaths, they did not appear to be in distress, and looked "to be in good health and alone."

But that might have changed in the days that followed — Shea said "there was a strong possibility money was running out" because the older sister had maxed out her credit card.

Police said a witness said he saw the pair in a playground near the river in Manhattan's Riverside Park on the morning their bodies were found. They were sitting about 30 feet away from each other with their hands in their heads. They appeared to be praying.

Shea said the witness, who appeared to be credible, described the scene as "haunting."'

Shea noted "you could walk right into the water" from near the area they were seen.

NYPD investigators said on Thursday that the sisters appear to have been alive when they entered the river, because their lungs were filled with water and there were no obvious signs of trauma. The medical examiner's office is investigating the cause of death. A law enforcement official told NBC News that suicide remains “a leading theory."

The pair had arrived in the United States with their mother and brothers — all citizens of Saudi Arabia — in 2015, according to police.

"The citizens were students accompanying their brother in Washington," the Saudi Consulate General said in a statement earlier this week.

Adding to the mystery, the Associated Press reported that their mother told detectives that on the day before the bodies were discovered, she received a call from an official at the Saudi Arabian Embassy, ordering the family to leave the U.S. because the daughters had applied for political asylum.

Shea said Friday he could not confirm that report, and that he's not sure of the parents' present whereabouts.

The Saudi's Consulate General in New York said in their statement earlier in the week that it had "appointed an attorney to follow the case closely."