The State Dept. did not provide any specific details regarding the cause of her death. Eygi was a Turkish-American dual national.
Reuters reported that Eygi was allegedly shot in the head by troops with the Israeli Defense Forces (IDF), citing reports from the official Palestinian news agency WAFA. She was transported to the hospital in critical condition.
"We tried to perform a resuscitation operation on her, but unfortunately she died," Fouad Nafaa, the head of the Rafidia Hospital in Nablus, told Reuters.
The Israeli military is investigating the report.
"Today (Friday), during Israeli security forces activity adjacent to the area of Beita, the forces responded with fire toward a main instigator of violent activity who hurled rocks at the forces and posed a threat to them," the IDF said in a statement.
"The IDF is looking into reports that a foreign national was killed as a result of shots fired in the area. The details of the incident and the circumstances in which she was hit are under review," the IDF added.
The US State Department said in a statement to Fox News: "We are urgently gathering more information about the circumstances of her death and will have more to say as we learn more. We have no higher priority than the safety and security of American citizens."
Turkey's foreign ministry condemned the death in a statement, alleging "murder committed by the Netanyahu government."
"Israel is trying to intimidate all those who come to the aid of the Palestinian people and who fight peacefully against the genocide," the statement reads. "This policy of violence will not work. The Israeli authorities who commit crimes against humanity and those who unconditionally support them will be held accountable before international courts."