The Palestinian National Authority said it would not allow Israel to look at the bullet that killed the journalist.
The results of the Palestinian Authority's investigation will be made public to the family, official authorities and the U.S., according to Hussein al-Sheikh.
The Palestinian National Authority President said the killing would be referred to.
Israel walked back its original claims that Abu Akleh likely died as a result of Palestinian gunfire, claiming later in the day that it could not determine who shot her.
The death of Abu Akleh was called an insult to media freedom by a State Department spokesman.
The Secretary-General of the United Nations was appalled by the killing and called for an investigation.
Abbas said that the Israeli occupation authorities were responsible for her killing and that they would not be able to hide the truth.
One of the first and most well-known field correspondents covering the Israeli-Palestinian conflict was Abu Akleh. The Palestinian-American reporter was killed and another journalist was injured while covering an Israeli raid in the West Bank town of Jenin. In response to a wave of deadly Palestinian attacks, Israeli forces have stepped up military operations in the West Bank. A reporter for al-Quds was shot by Israeli security forces and was wearing a blue flak jacket. The journalists were hit by Palestinian gunfire. An initial autopsy carried out by the Institute of Pathology at An Najah University found that Abu Akleh was shot at a range of more than one meter, but did not offer any conclusions about who fired the bullet.
According to the Committee to Protect Journalists, at least 18 journalists have been killed in Israel and the Palestinian Territories since 1992.
Palestine rejects the Israeli probe into Abu Akleh's killing.
A journalist was shot and killed while covering a raid.
A reporter for Al Jazeera was killed in the West Bank.