Israel has told the US that they are in the "final stages" of an investigation into the killing of Turkish-American activist Aysenur Ezgi Eygi by Israeli forces in the occupied West Bank in September, the State Department said.

"They have told us that they are in the final stages of closing their investigation," State Department spokesperson Matthew Miller told reporters during a briefing at the State Department's Foreign Press Center on Tuesday.

"We want to be briefed on the results of it. We want to know exactly what happened and why it happened and who was involved, and what Israel is doing to make sure such incidents don't happen again," he added.

Miller said the US made clear to Israel that the killing of Eygi was "unacceptable" and "never should have happened."

"She was there attending a peaceful protest, and we want to see answers. We want to give her family answers," he added.

US Secretary of State Antony Blinken "met with her family yesterday because they have a right to know, they have a right to demand accountability, and we share their demands for it," Miller said.

Same rhetoric

Eygi's family expressed frustration after meeting with Blinken on Monday at the State Department, saying they heard the "same things" without meaningful action.

"Secretary (Blinken) was attentive in listening to us and unfortunately repeated a lot of the same things that we've been hearing for the past 20 years, particularly since (American activist) Rachel Corrie's killing, who is also a Washington state resident like my wife. It's frustrating to hear the same things again," Eygi's husband, Hamid Ali, told reporters after the meeting.

"We hope that things will be different this time around. But as I said, our expectations are what they are," he said, repeating the family's call for a US-led investigation into her killing.

Ozden Bennett, Eygi's sister, said the family does not find the Israeli investigation "credible."

"He (Blinken) listened to our frustrations, which were long, and at this point, we did leave asking Secretary of State Blinken to push publicly and put pressure on the Israeli government at the very least to finish their investigation into my sister's killing before the changeover in the administration," she said.

Deliberate killing

Aysenur Ezgi Eygi, 26, a dual Turkish and US citizen, was killed by Israeli forces on September 6 during a peaceful protest against illegal Israeli settlements near Nablus in the occupied West Bank.

A preliminary investigation by Israel found that Eygi was "highly likely" hit "indirectly and unintentionally" by Israeli fire that was targeting a "main instigator of violent activity who hurled rocks" during the protest.

Video evidence and witness accounts, however, have contradicted Israel's version of events, with many saying an Israeli sniper directly shot her.

A report by The Washington Post also revealed that Eygi was shot more than 30 minutes after the peak of confrontations in Beita and about 20 minutes after protesters had moved over 200 yards down the main road, away from Israeli soldiers.