The Israeli military says a US observer would be present for the procedure that could deliver results within hours.
The Palestinians, who on Saturday handed over the bullet to a US security coordinator, said they had been assured that Israel would not take part in the ballistics.
Washington has yet to comment. The United States has a holiday weekend to mark July 4.
The May 11 death of the Al Jazeera reporter 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 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.
"The (ballistic) test will not be American. The test will be an Israeli test, with an American presence throughout," said Israeli military spokesman Brigadier-General 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."
Akram al-Khatib, general prosecutor for the Palestinian Authority, said the test would take place at the US Embassy in 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 will be a diplomatic and domestic test for new 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.
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