Washington DC - The US wants Israel to conduct a "thorough" investigation into its own soldiers' killing of a Turkish-American citizen in the West Bank last week, the State Department said on Monday.

"We have urged a swift, thorough, and transparent investigation and are urgently working to get more information as possible as it relates to the circumstances of her death," State Department spokesman Vedant Patel told journalists.

Aysenur Ezgi Eygi (26) was "shot in the head" while participating in a demonstration in Beita in the West Bank on Friday, the United Nations rights office has said.

The Israeli military said its forces "responded with fire toward a main instigator of violent activity who hurled rocks at the forces and posed a threat to them" during the protest.

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

The group on Saturday dismissed claims that ISM activists threw rocks at Israeli forces as "false" and said the demonstration was peaceful.

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.