The family of a Turkish American woman shot by the Israeli military while attending a protest in the West Bank have been joined by a growing chorus of US lawmakers demanding that their government launch its own investigation into the killing.

Autopsies conducted in the West Bank town of Nablus and Turkey found that Ayşenur Ezgi Eygi was shot in the head. Shortly after the incident, the Israeli Defense Forces (IDF) said in a statement that it was “highly likely that she was hit indirectly and unintentionally by IDF fire which was not aimed at her”.

The White House has called for Israel to investigate Eygi’s death but friends and family has expressed skepticism that such an inquiry will lead to any accountability.

“We are not putting our faith or trust in a military that deliberately shot and killed an individual to investigate themselves of their own crime,” said Juliette Majid, who graduated alongside Eygi from the university of Washington in Seattle.

“What I want is justice and accountability, which to me looks like a US-led criminal investigation … I want the US to hold [the Israeli military] accountable. At the end of the day, we shouldn’t be in this situation, Ayşenur should be coming home alive,” she said.

Eygi’s family’s call for a US-led inquiry has been echoed by senator Patty Murray and congresswoman Pramila Jayapal of Washington state who wrote to Joe Biden and the US secretary of state, Antony Blinken, demanding that the Federal Bureau of Investigation (FBI) launch an investigation.

“We fear that if this pattern of impunity does not end with Ms Eygi, it will only continue to escalate,” they said, pointing to the killing of activist Rachel Corrie – also from Washington state – in 2003 at a protest in Gaza, and calling on the US government to better protect American citizens overseas.

Murray and Jayapal demanded a written response from the Biden administration by 24 September addressing their calls for an independent investigation, what the US government knew about her killing and how it would protect US citizens overseas.

With no apparent response from the administration, more than 100 members of congress – including leading Democratic party officials Alexandria Ocasio-Cortez and Eric Swalwell as well as senator Bernie Sanders – have sent a second letter to Biden, Blinken, and the US attorney general, Merrick Garland, demanding a US-led investigation .

“Given the evidence, we believe the United States must independently investigate whether this was a homicide. To walk away without asking further questions gives Israeli forces unacceptable license to act with impunity,” they wrote. “There must be accountability for Ms Eygi’s death.”

The lawmakers demanded a written report to Eygi’s family, delivered by 4 October, including details of whether the US government will investigate her killing and a timeline for the inquiry, as well as how the US government would respond should the Israeli government refuses to cooperate with their investigation.

“I hope the US government is listening not just to their own officials who represent their constituents, but also the general public who want to see justice for a US citizen murdered abroad,” said Majid.

She added that promises by Turkey to launch an investigation through the public prosecution in Ankara provided “a little bit of hope”, but that she and Eygi’s family want to see the US government wield its influence.

“I want to see my own government step up,” she said.

Eygi was born in Turkey but she and her parents moved to Washington state when she was a child. The 26-year-old was buried in her family’s hometown on the Turkish coast earlier this month.

The US president, meanwhile, has yet to contact Eygi’s family. “I think it’s incredibly shameful that president Biden in particular hasn’t reached out to the family to offer his condolences at the very least, and at most promise justice and accountability for an American citizen,” said Majid. “He was supposed to be providing protection.”