However, Hamas on Friday 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.
An Israeli policewoman was stabbed and killed in the attack, police said, with security forces shooting dead three Palestinian assailants.
Israel's security services have reported IS-inspired attacks in the past and arrested those suspected of links to the jihadist group, but this is the first direct claim by IS on Israeli soil.
However Hamas and People's Front for the Liberation of Palestine terror groups quickly retorted that the three attackers, who were later shot and killed by Israeli officials were their members.
A 20 year-old Israeli border guard is in critical condition in a Jerusalem hospital, and several civilians are injured after two simultaneous knife and gun assaults in the historic city center.
Friday's deadly attack affected thousands of families across the West Bank who planned to visit relatives over the Ramadan holiday.
On Tuesday, US Secretary of State Rex Tillerson said the Palestinian Authority had agreed to halt payments to the families of slain attackers, including suicide bombers.
The acronym PFLP stands for the Popular Front for the Liberation of Palestine, a long-in-the-tooth terrorist organization formed after the 1967 war between Israel and Egypt, now a branch of the Palestinian Authority in the West Bank.
The Israeli army said the assailants appeared to have acted independently, like numerous attackers in unrest that has rocked Israel and the occupied territories since October 2015.
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"I have instructed the police to reinforce security arrangements and checking procedures in the plaza around Damascus Gate", Netanyahu said at a weekly cabinet meeting, explaining that he was consdiering making the zone a "sterile area".
The ISIS terrorist group claimed responsibility for the attack, their first on Israeli soil, however it is not clear if the attackers were aligned with them or not.
The assailants, all from the West Bank village of Deir Abu-Mashal near Ramallah, were shot and killed by the police.
Rosenfeld added that no restrictions are being enforced against Palestinians from the West Bank who have procured legal permits to enter Jerusalem, and that no age restrictions for men allowed to enter the Temple Mount are being imposed.
Thirty-eight Israelis, two American tourists and a British student have been killed in shootings, car-rammings and stabbings since a wave of Palestinian street attacks began in October 2015.
Some Israeli media later said that ISIS had claimed responsibility.
Israeli authorities also denied ISIS involvement.
The area around Damascus Gate was sealed off in the hours after the attack, with a few youths throwing fireworks at security forces.
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