Latest Updates: Israeli Police Attack Mourners at Palestinian Journalist’s Funeral

The bullet that killed the Palestinian American journalist Shireen Abu Akleh on Wednesday has become a central point of contention in the competing efforts by Israelis and Palestinians to investigate who shot her.

The Palestinian Authority on Thursday declined a request to let Israeli officials examine the bullet that killed Ms. Abu Akleh, a prominent reporter for Al Jazeera who was killed in the occupied West Bank during an Israeli raid.

The authority said it would investigate Ms. Abu Akleh’s death independently, rejecting Israeli calls for a joint inquiry and for the bullet to be assessed in an Israeli laboratory under international supervision.

Palestinian officials and witnesses accused Israeli soldiers of killing Ms. Abu Akleh, dismissing Israeli claims that the journalist may have been hit by Palestinian fire during a shootout in Jenin, a city in the northern West Bank.

Palestinian leaders said that Israel could not be trusted to investigate the killing, while Israeli officials said that the Palestinians had refused to provide the bullet in order to hide the truth.

The bullet has become the focus of two competing narratives about the circumstances of her death. Witnesses said Ms. Abu Akleh was shot by Israeli soldiers in an area of Jenin where there were no Palestinian gunmen. But Israeli military officials said she was struck during a shootout between Israelis and Palestinians, and that she had been in the vicinity of a Palestinian armed with an assault rifle.

Video from the scene did not show the moment when the bullet hit Ms. Abu Akleh, or who fired it.

Both Israeli soldiers and Palestinian militants involved in the Jenin clashes were carrying M16 assault rifles, guns that use the same 5.56-millimeter bullets, Israeli officials said.