Police are investigating the deaths of two sisters from Saudi Arabia whose bodies, bound together with tape, washed up on New York City’s waterfront last week.

The sisters, Tala Farea, 16, and Rotana Farea, 22, were discovered on 24 October on a bank of the Hudson river, on the west side of Manhattan. But they lived in Fairfax, Virginia, about 225 miles away, from where they were reported missing in August.

As of Tuesday investigators had not determined the circumstances surrounding their fate, and the medical examiner’s office in New York had not yet released a cause of death. The sisters’ bodies were taped together and facing each other, but had no obvious signs of trauma, police said. They were both fully clothed.

The day before the bodies were discovered on 24 October, the sisters’ mother told detectives that she had received a call from an official at the Saudi Arabian embassy in Washington, ordering the family to leave the US because her daughters had applied for political asylum, New York police said on Tuesday.

Saudi Arabia’s consulate general in New York said in a statement that it had “appointed an attorney to follow the case closely”. It said embassy officials in Washington had contacted the family and “extended its support and aid in this trying time”. It added that the sisters were students “accompanying their brother in Washington”.

The case has immediately heightened tension over relations with Saudi Arabia in the aftermath of the killing of Saudi dissident and Washington Post journalist Jamal Khashoggi at the Saudi embassy in Istanbul earlier this month.

New York City police department has sent a detective to Virginia to learn more about the sisters. Chief of detectives Dermot Shea said they were particularly interested in finding out what happened since they were reported missing, and what led them to New York City. “We are looking at all clues in their past life,” Shea said.

Tala and Rotana moved to the US from Saudi Arabia with their mother in 2015, settling in Fairfax, a suburb of Washington DC, police said.

Rotana was enrolled at George Mason University, but left in the spring. A George Mason spokesman called the news of her death “tragic” and said the university was cooperating with police.

Police said the sisters left their family home and were placed in a shelter after an earlier disappearance in December 2017. They were reported missing again on 24 August.

Police initially struggled to identify the bodies, as last week many of the city’s and the country’s law enforcement agencies were racing against time to find the domestic terrorist responsible for package bombs sent to a dozen prominent Democrats and CNN’s New York City bureau.

Police released sketches of the sister’s faces and posted repeated calls for the public’s help in identifying them on social media. “We are out to get justice for those two girls and find out exactly what happened,” Shea said. On Wednesday afternoon, the NYPD issued photographs of the sisters.