The body of Aysenur Ezgi Eygi (also inset) lies in a hospital morgue in Nablus on Friday. AFP

Aysenur Ezgi Eygi, 26, was "shot in the head" while participating in a demonstration in Beita in the West Bank on Friday.

"Her presence in our lives was taken needlessly, unlawfully, and violently by the Israeli military," Eygi's family said in a statement.

"A US citizen, Aysenur was peacefully standing for justice when she was killed by a bullet that video shows came from an Israeli military shooter.

"We call on President (Joe) Biden, Vice President (Kamala) Harris, and Secretary of State (Antony) Blinken to order an independent investigation into the unlawful killing of a US citizen and to ensure full accountability for the guilty parties."

This undated family photo provided by ISM on Friday, shows Aysenur Ezgi Eygi of Seattle. AP

Eygi was a member of the International Solidarity Movement (ISM), a pro-Palestinian organisation, and was in Beita on Friday for a weekly demonstration against Israeli settlements, according to ISM.

In recent years, pro-Palestinian demonstrators have frequently held weekly protests against the Eviatar settlement outpost overlooking Beita, which is backed by far-right Israeli ministers.

During Friday's protest, Eygi was shot in the head, according to the UN rights office and Rafidia hospital where she was pronounced dead.

Turkey said she was killed by "Israeli occupation soldiers," with President Recep Tayyip Erdogan condemning the Israeli action as "barbaric."

Washington called it a "tragic" event and has pressed its close ally Israel to investigate. But her family has demanded an independent probe.

"Given the circumstances of Aysenur's killing, an Israeli investigation is not adequate," her family said. Her family said Eygi always advocated "an end to the violence against the people of Palestine."

Agence France-Presse