US officials have insisted that a ceasefire in Gaza is close even as fighting rages unabated in the blockaded Palestinian territory and violence spirals in the occupied West Bank, where witnesses told the Observer an American-Turkish dual national was killed by Israeli forces on Friday. William Burns, who is also the US’s chief negotiator in the indirect talks between Israel and Hamas, echoed secretary of state Antony Blinken during a speech in London on Saturday in which he said that “90% of the text had been agreed but the last 10% is always the hardest”. But pressure from the US, Israel’s most important ally, and the two mediators speaking to Hamas, Qatar and Egypt, has done little to assuage the fighting in Gaza or rising tensions in the West Bank. The US has also said it is urgently seeking more information about the killing of Ayşenur Ezgi Eygi, 26, who witnesses said was shot in the head by Israel Defence Forces (IDF) troops during an anti-settlement protest in the West Bank on Friday. Several of Israel’s western allies, including the US, have recently imposed sanctions on individuals and organisations associated with Israel’s settler movement, despite blowback from prime minister Benjamin Netanyahu’s ­government, which includes far-right supporters of Israeli extremism in the West Bank. Eygi’s family have called for an independent investigation into her killing, adding to the pressure on the Biden administration to end what critics say is US complicity in the Israeli occupation. On Saturday, IDF troops, some of whom appeared to be forensic investigators, visited the town of Beita, near Nablus, to examine the scene where Eygi was killed. For the residents, it was yet another case of the IDF investigating itself: about 1% of army inquiries result in prosecutions, according to rights groups. All of the Beita residents the Observer spoke to gave very similar accounts of the shooting. A group of demonstrators had gathered on the hillside, as they have every Friday for midday prayers in recent years, to protest against Eyvatar, an Israeli settlement on the next hill built on land belonging to Palestinian farmers. On this occasion, there were some 20 Palestinians from Beita, 10 foreign volunteers from the anti-occupation International Solidarity Movement, including Eygi, and about a dozen children from the district. “The kids were throwing stones here at the junction, and the soldiers fired tear gas at them,” Mahmud Abdullah, a 43-year-old resident said. “Everyone scattered and ran into the olive grove and then there were two shots.” One of the bullets hit something along the way and a fragment hit a protester in the stomach, wounding him slightly, the witnesses said. The other bullet hit Eygi in the head, passing through her skull. Neighbours pointed out both the spot where Eygi was shot and where the bullet came from: a house on a ridge. The owner, Ali Mohali, said a group of soldiers, perhaps half a dozen, had gone on to his roof, 200m from where Eygi was shot. He said he heard one shot, but was not sure if there had been a second from that position. The IDF statement on the incident said it was looking into the report that troops had killed a foreign national while firing at an “instigator of violent activity who hurled rocks at the forces and posed a threat to them”. Moneer Khdeir, Mohali’s 65-year-old neighbour, was derisive of the IDF account. “They said that the stones posed a threat to the soldiers. They were stones thrown by kids from all the way down there, yet they talk about it like it was a Yassin [rocket propelled grenade],” Khdeir scoffed. Across the West Bank, army units on the ground are increasingly seen by Palestinians as a protective military wing of the settlers, taking their cues from the far right elements of Netanyahu’s government. Palestinian officials and rights groups have long accused the IDF of standing by during or even joining in settler attacks. Hisham Dweikat, 57, a science professor from Beita, said Eygi was the 15th person to be killed protesting against Eyvatar over the three years since the settlement was reoccupied, but hers was the first killing the IDF has investigated. He did not put much faith in the result. “It is clear that the army is with the settlers,” he said. Fifteen kilometres south of Beita in the village of Qaryut, Amjad Bakr and his family buried his 12 year-old daughter Bana on Saturday afternoon. She was shot dead while opening the window in her bedroom at about the same time on Friday that Eygi was killed in Beita. “As usual on Friday, settlers came to raid the town and the people of the town went to defend themselves. There was a confrontation and the army came,” said Bakr, 47. “We went back home, because we thought that if the army was here, maybe they could stop the settlers. But unfortunately the army did not stop the settlers. They stand with the settlers,” he said. “The bullet that hit my daughter came through the window and hit her in the heart,” he said. “She was innocent, and shy, and clever. She had memorised three sections of the Holy Quran.” As to what Bana had planned to do with her life, Bakr shrugged: “An Israeli bullet doesn’t care about the future of any Palestinian.” In a statement, the IDF said that soldiers were dispatched to disperse violent confrontation between dozens of Palestinians and Israelis, and had fired shots in the air. “A report was received regarding a Palestinian girl who was killed by shots in the area. The incident is under review,” it said. Since Hamas’s 7 October assault that triggered the war in Gaza, Israeli troops or settlers have killed at least 662 Palestinians in the West Bank, according to the Palestinian health ministry, which does not differentiate between militant and civilian deaths. The toll is almost five times higher than the 146 killed in 2022, which was already an almost 20-year record high. At least 23 Israelis, including security forces, have been killed in Palestinian attacks during the same period, according to Israeli officials. Meanwhile, in the Gaza Strip, another 61 people were killed in Israeli airstrikes across the territory in the past 48 hours, the health ministry in the Hamas-run territory said, putting the death toll at 40,939 people. Around 1,200 Israelis and other nationals were killed in Hamas’s 7 October assault that triggered the war, according to Israeli tallies. The latest round of ceasefire talks have stalled over Netanyahu’s insistence that Israeli troops will not withdraw from the Gaza-Egypt border – a dealbreaker for Hamas – despite agreeing to the measure in talks held in July. Tensions between Israel and its regional foes - Iran and the powerful Lebanese militia Hezbollah - have brought the Middle East to the brink of regional war on several occasions in the past 11 months.