"Two police officers were critically injured and later died of their wounds in an Israeli hospital, while a third one was hurt by shrapnel and is out of danger", police said.
The closure prompted hundreds of Muslim worshippers to gather outside the walled Old City gates and hold prayers there.
Police recovered two locally made automatic rifles, a pistol and a knife, police spokesman Micky Rosenfeld told AFP. In the courtyard of the compound a final gun battle ensued between the gunmen and Israeli security forces.
A relative, Yehiyeh Jabareen, says clan members are in shock over Friday's attack at the holy site, a walled compound revered by both Muslims and Jews.
The Israeli authorities are still trying to work out the identities of the attackers.
Jordan is exerting its utmost efforts to pressure Israel to reopen al-Aqsa Mosque which Israel closed on Friday for the first time in 50 years following a gun attack that killed two Israeli policemen.
"Security assessments [are] being carried out by police officers and police commissioner".
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The site, which contains the Al-Aqsa Mosque, is controlled by a Jordanian-Palestinian waqf, or Islamic trust, in a policy that has remained since Israel captured the territory during the 1967 Six-Day War. He called upon all to act responsibly to avoid escalation.
A statement from Netanyahu's office confirmed the call.
The gunmen had opened fire on the patrol near the Lion's Gate area of the Old City before fleeing to the holy site.
Following the incident, access to nearby mosques for Friday prayers were banned, Israeli police said.
Israel's Public Security Minister Gilad Erdan said the attack was "a serious and severe event in which red lines were crossed", adding that security arrangements in and around the site would be reviewed. "All must take a stand against terror & condemn it".