A US forensic team has already arrived in Palestine to carry out the test, a senior Palestinian official says.
Palestinian Attorney-General Akram al Khatib has said that a US team will examine the bullet that killed Al Jazeera journalist Shireen Abu Akleh.
"A US team has already arrived to conduct the forensic examination of the bullet at the US Embassy in [West] Jerusalem," al Khatib told the official Palestine Voice radio on Sunday.
He said the bullet will be returned to the Palestinians after the examination, adding that there will be no Israeli participation in the analysis.
"The bullet will never be given to the Israeli side for examination," he added.
The statement from Palestine official came after an Israeli military official said earlier that will test the bullet.
"The (ballistic) test will not be American. The test will be an Israeli test, with an American presence throughout," Israeli military spokesperson Brigadier-General Ran Kochav said on Sunday.
"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."
The May 11 death of Al Jazeera reporter Shireen Abu Akleh during an Israeli raid in the occupied West Bank, and feuding between the sides as to the circumstances, have overshadowed a visit by US President Joe Biden to Israel due this month.
The Palestinians accuse the Israeli military of killing her deliberately. Israel denies this, saying Abu Akleh may have been hit by errant army fire or by one of the Palestinian gunmen who were clashing with its forces.
Akram al Khatib, general prosecutor for the Palestinian Authority, said the test would take place at the US Embassy in West Jerusalem.
"We got guarantees from the American coordinator that the examination will be conducted by them and that the Israeli side will not take part,” al Khatib told Voice of Palestine radio, adding that he expected the bullet to be returned on Sunday.
An embassy spokesperson said: "We don't have anything new at this time."
Biden is expected to hold separate meetings with Palestinian and Israeli leaders on July 13-16.
The Abu Akleh case appears to be a diplomatic and domestic test for new caretaker Israeli Prime Minister Yair Lapid. Israeli Deputy Internal Security Minister Yoav Segalovitz said 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," Segalovitz told Army Radio.
So far, the UN as well as journalists at The New York Times, CNN and The Washington Post have determined that an Israeli soldier shot to kill Abu Akleh. Abu Akleh was wearing a press vest when she was shot in the face by a single bullet.