A military official said the source of the shot is still unclear but “we have narrowed down the IDF weapon that might be involved in the fire exchange near Shireen”.
Israel has asked Palestinians to turn over the bullet for analysis, AP reported.
Abu Akleh was fatally shot on May 11 while covering an Israeli military raid in the occupied West Bank.
Palestinian officials, along with fellow journalists who were with Abu Akleh, said Israeli troops stationed nearby killed her.
The Israeli army said she was shot during a battle between troops and Palestinian gunmen but said it could not be determined who fired the fatal bullet without a proper analysis.
Israel has called for a joint investigation with the Palestinians.
The Palestinians have refused to hand over the bullet, saying they do not trust Israel. They said they are conducting their own investigation and are ready to co-operate with any country except Israel.
The military last week released the results of a preliminary investigation that offered two possible causes of death. It said that in one scenario she may have been hit by Palestinian gunfire during a fierce shoot-out with Israeli troops.
In the second, it said she might have been hit by an Israeli soldier who shot through a “designated firing hole” in a military vehicle at a Palestinian gunman who was shooting at the vehicle. It said it could not determine the source of fire without analysing the bullet.
The military official confirmed that investigators have turned their focus to a specific weapon.
He said if the Palestinians co-operate with the investigation, Israel will “hopefully be able to compare the bullet to that barrel and check if there is a match.” He spoke on condition of anonymity under military briefing guidelines.
The Palestinians have been conducting their own investigation. Last Friday, the Palestinian public prosecutor said preliminary findings show Abu Akleh was killed by deliberate fire from Israeli troops. The prosecutor said the investigation would continue.
Bellingcat, an independent Dutch-based open-source research firm, has conducted its own analysis of material gathered largely from videos on social media. It said its initial findings lent support to Palestinian witnesses who say she was killed by Israeli fire.
Abu Akleh, a Palestinian-American and 25-year veteran of Al Jazeera, was killed in the Jenin refugee camp in the northern West Bank. She was a household name across the Arab world, known for documenting the hardship of Palestinian life under Israeli rule, now in its sixth decade.
The shooting drew condemnations and statements of concern from around the world. Israel has also been widely criticised for the behaviour of its police, who pushed and beat mourners at Abu Akleh's funeral last Friday, causing the pallbearers to nearly drop her coffin.