U.S. Secretary of State Antony Blinken and Defense Secretary Lloyd Austin on Tuesday demanded an overhaul of Israeli military conduct in the occupied West Bank as they decried the fatal shooting of an American protester against settlement expansion, which Israel said was accidental.

Aysenur Ezgi Eygi, 26, who is also a Turkish national, was shot dead last Friday at a protest march in Beita, a village near Nablus where Palestinians have been repeatedly attacked by far-right Jewish settlers.

Israel's military said on Tuesday that its initial inquiry found it was highly likely its troops had fired the shot that killed her but that her death was unintentional, and it voiced deep regret.

President Joe Biden later told reporters "it ricocheted off the ground" and a U.S. official said that was the conclusion of the Israeli investigation, the results of which were presented to the United States on Tuesday.

Palestinian officials say that Eygi was struck in the head.

Eygi's family called Israel's preliminary inquiry "wholly inadequate" and demanded an independent U.S. investigation.

Hamid Ali, Eygi's partner, in response to Biden's comments, said her death "was no accident and her killers must be held accountable."

"The White House has not spoken with us. For four days, we have waited for President Biden to pick up the phone and do the right thing," Ali said.

Blinken and Austin, in their strongest comments to date criticising the security forces of Washington's closest Middle East ally, described Eygi's killing as "unprovoked and unjustified". They separately said said Washington would insist to the Israeli government that it makes changes to how its forces operated in the West Bank.

"No one should be shot and killed for attending a protest. No one should have to put their life at risk just for freely expressing their views," Blinken told reporters in London.

"In our judgment, Israeli security forces need to make some fundamental changes in the way that they operate in the West Bank, including changes to their rules of engagement.

"Now we have the second American citizen killed at the hands of Israeli security forces. It's not acceptable," Blinken said.

An Israeli government spokesperson declined to comment on Blinken's remarks.

Austin spoke to Israeli Defense Minister Yoav Gallant, the Pentagon said late on Tuesday, adding he expressed "grave concern for the IDF's responsibility for the unprovoked and unjustified death" of Eygi. He also urged Gallant "to reexamine the IDF's rules of engagement while operating in the West Bank," according to the Pentagon.

The Israeli military earlier said an investigation by the Military Police Criminal Investigation Division was under way and its findings would be submitted for higher-level review once completed.

"We're going to be watching that very, very closely," White House national security spokesperson John Kirby told reporters, saying a criminal probe was an unusual step by Israel's military.

"We're going to want to see where it goes now in terms of the criminal investigation and what they find, and if and how anyone is held accountable," Kirby added.