Missing Israelis Mali and Liel Yahalomi reportedly traveled from Austria to Germany before boarding a flight to Argentina, a significant development that appears to shed new light on the mysterious disappearance of the mother and daughter.

Israeli media reported Friday evening that the two left Vienna aboard a train bound for Germany and subsequently took a flight from Germany to Argentina.

While authorities have not officially established where Mali and Liel are currently located within Argentina, investigators have reportedly confirmed that the pair purchased airline tickets and boarded the flight from Germany.

The development came after Austrian police confirmed earlier Friday that the mother and daughter had departed Austria on their own. Authorities said there was currently no indication that the pair had been victims of a violent crime.

According to Austrian media reports, Vienna police checked local hospitals and conducted internal inquiries in an effort to determine what had happened to the two women. Police did not, however, launch an official public missing-person search because authorities determined there were insufficient legal grounds to do so.

Israeli investigators also reported making headway Friday in reconstructing the movements of Mali and Liel before their disappearance from contact.

“We have made progress in mapping out the pair’s timeline and activity,” Israel Police sources said.

Investigators have reportedly succeeded in establishing additional details about the pair’s movements and activities, helping close some of the gaps in the timeline surrounding the case.

“We hope there will be a breakthrough soon,” the sources added.

The developments followed days of intense speculation over what might have happened to the mother and daughter. Earlier, their family appealed to Israeli security and law enforcement authorities not to dismiss any possible explanation until it had been thoroughly investigated.

“For a week now, we wake up every morning with the same prayer – to find you safe and sound and bring you home. Please do not stop searching,” the family said.

Relatives added that they “demand all security and investigative authorities continue examining all potential scenarios, including the possibility of a terror-related motive, until it is definitively ruled out based on concrete findings.”

New surveillance footage obtained during the investigation also provided important evidence about the pair’s departure from their accommodations in Vienna. The video shows Mali and Liel leaving the apartment building where they had been staying while carrying their personal belongings. No other individual can be seen accompanying them.

Before reports emerged that the two had traveled onward to Argentina, a senior official familiar with the investigation said Friday that authorities believed Mali and Liel remained alive. At the time, however, investigators still had not determined why they had disappeared or stopped communicating with those searching for them.