Hamas on Saturday said the three Palestinians shot dead in Jerusalem after the fatal stabbing of an Israeli policewoman belonged to local Islamist and leftist movements, rejecting an earlier claim by the Islamic State group.

"The claim by the Islamic State group is an attempt to muddy the waters," said Sami Abou Zouhri, spokesman for the Islamist movement which runs the Gaza strip.

The attack was carried out by "two Palestinians from the Popular Front for the Liberation of Palestine and a third from Hamas", he said.