Shireen Abu Akleh suffered a gunshot wound to the head in Jenin on Wednesday. Al Jazeera and Qatar, where the news networkd is based, accused Israeli troops of the killing.
Israel, which has voiced regret at Abu Akleh's death, said it was looking into the killing and that the fatal shot might have been fired by a Palestinian gunman.
It has proposed a joint investigation with the Palestinians, asking them to provide the bullet for examination.
"We rejected the joint investigation with the Israeli occupation authorities because they committed the crime and because we don't trust them," said Abbas during an official memorial ceremony for Abu Akleh, who was Palestinian-American.
He added that the Palestinian Authority "will go immediately to the International Criminal Court in order to track down the criminals".
Abu Akleh, 51, was wearing a blue vest clearly marked "Press" while reporting in Jenin, Al Jazeera said. She was covering the latest arrest operation launched by the Israeli military amid deadly Arab attacks in Israel. Another Palestinian journalist at the scene, Ali Samoodi, was wounded.
The body of Abu Akleh was driven in a motorcade from a hospital in the Palestinian hub city of Ramallah towards Abbas's compound. Hundreds of mourners lined both sides of the road, some throwing flowers.
The death drew international and Arab condemnation, including from the White House, which demanded a "comprehenisve investigation".
