Shea said the police are continuing to look for, and through, credit-card, phone and other records to try to fill out the timeline of their whereabouts.
The girls' mother also told detectives her daughters were applying for political asylum in the U.S.
Police say there were no signs of trauma and it appeared that they were alive when they went into the water.
The sisters, originally from Saudi Arabia, were found clothed in fur trim coats and bound together with duct tape.
The bodies were identified as the sisters on October 27. The cause of their deaths has yet to be determined.
Tala Farea had been missing from Fairfax since August 24, according to the National Center for Missing and Exploited Children.
"I can't talk about it", she said.
How did they end up in NY?
It's unclear when the women arrived in NY and where they were staying, the sources said.
They always order two meals from room service, officials said.
What did the sisters do before their deaths?
The area they were found was "such a place where you would essentially walk right into the water", he said.
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.
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Detectives spent the last week interviewing family members in Virginia and trying to piece together the sisters' movements in recent months.
CCTV footage showed that the sisters were in good health before their death, and had stayed at a number of high-end hotels in the city.
Did anyone see them just before they died?
This past Wednesday, a man described as a credible source contacted investigators about something that had been "haunting him", Shea said.
The witness said he was exercising at about 7 a.m. the day the Farea sisters' bodies were discovered.
A witness claims to have seen the sisters praying near the Hudson River on the morning of October 24th.
It wasn't the first time the sisters vanished.
"We are still investigating the full details within this case".
Were the girls seeking asylum?.
"We also have the sources that the detectives have developed from this investigation thus far; statements made that they would rather inflict harm on themselves and commit suicide than return to Saudi Arabia", Shea said. "We treat everything like a crime until we know otherwise", he said.
They had recently applied for asylum in the U.S. after arriving in 2015.
"Reports we ordered anyone related to the Saudi sisters to leave the USA for seeking asylum are absolutely false", Fatimah Baeshen said on Twitter on Saturday.
HuffPost could not independently confirm this, and the Department of Homeland Security did not immediately respond to a request for comment.