Forensic investigators are expected to confirm that the bullet was fired from an Israeli army rifle, the central claim of a Palestinian Authority investigation into the killing.
But on Sunday, Israel claimed that their own investigators, rather than the Americans, would examine the bullet, with an American present during the test of the fired round.
The Israeli claim provoked a strong response from Mr Khatib, who said the Palestinian Authority had been given assurances that the Israelis would not be involved in this final part of the probe.
The Palestinian-American journalist, who had covered the Israel-Palestine conflict for 25 years, was struck in the head by a bullet on May 11 during a gun battle between Israeli soldiers and Palestinian militants. She had been reporting on an Israeli army raid with colleagues early that morning. The team of Al Jazeera journalists wore blue body armour and helmets emblazoned with the word “Press”.
An official Palestinian investigation into Abu Akleh's death concluded that she was killed by a bullet fired from an Israeli army Ruger Mini-14 rifle.
“Examination of the fired projectile revealed that it is a calibre of 5.56 millimetres and that it bears a mark and general and individual characteristics that match the general marks of the Mini-14 Ruger weapon, which is a semi-automatic sniper weapon,” Mr Khatib said of the initial investigation.
The Palestinian Authority was assured that no modifications would be made to the bullet and that it would be returned as soon as the assessment was complete, he told AFP.
The authority agreed to hand over the bullet to the US, but not to Israel, the official Wafa Palestinian news agency reported.
Israel however, has denied that the bullet will be examined by US investigators alone, saying it would also take part in the investigation.
Israeli officials said on Sunday that a US observer would be present for the procedure that could deliver results within hours.
Washington has yet to comment. The US has a long weekend to mark its independence day on July 4.
“The [ballistic] test will not be American. The test will be an Israeli test, with an American presence throughout,” said Israeli military spokesman Brig Gen Ran Kochav.
“In the coming days or hours it will be become clear whether it was even us who killed her, accidentally, or whether it was the Palestinian gunmen,” he told Army Radio. “If we killed her, we will take responsibility and feel regret for what happened.”
Mr Al Khatib said the test would take place at the US Embassy in Jerusalem.
“We got guarantees from the American co-ordinator that the examination will be conducted by them and that the Israeli side will not take part,” he told Voice of Palestine radio, adding that he expected the bullet to be returned on Sunday.
An embassy spokesman said: “We don't have anything new at this time.”
US Secretary of State Antony Blinken promised last month to pursue accountability over the killing of Abu Akleh wherever the facts might lead.
“We are looking for an independent, credible investigation. When that investigation happens, we will follow the facts, wherever they lead. It's as straightforward as that,” Mr Blinken said.
The UN rights office inspected photo, video and audio material, visited the scene, consulted experts, reviewed official communications and interviewed witnesses. “We find that the shots that killed Abu Akleh came from Israeli security forces,” UN Human Rights Office spokeswoman Ravina Shamdasani told reporters in Geneva.
“It is deeply disturbing that Israeli authorities have not conducted a criminal investigation.”
The probe examined submissions from the Israeli army and the Palestinian attorney general.
However, the Israeli army branded the UN's findings unfounded, insisting it was “not possible” to determine how Abu Akleh was killed.
US President Joe Biden is expected to hold separate meetings with Israeli and Palestinian leaders during his visit to the Middle East from July 13-16.
The Abu Akleh case will be a diplomatic and domestic test for new Israeli Prime Minister Yair Lapid.
Israel' deputy internal security minister Yoav Segalovitz said Mr Lapid had been involved in “managing the arrival and transfer of this bullet”.
“It will take a few days to conduct a ballistic test, with several experts, to ensure that there is an unequivocal assessment,” Mr Segalovitz told Army Radio.