The site has proved a tinder-box in the Israeli-Palestinian conflict in the past.
Harry Fawcett, a reporter for Al-Jazeera, claimed police said that the gunmen were armed with two machine guns as well as a pistol and a knife.
The Israeli measures, including CCTVs covering the entire compound, checkpoints and metal detectors at the entrances, were installed after three Palestinian Muslims with Israeli citizenship shot dead two Israel policemen on Friday morning.
Israel's police chief says the attackers used weapons stored inside the compound and opened deadly fire on a police patrol. But he also called on Netanyahu to reopen the holy site.
In an unusual move, Israeli security forces closed the site after the exchange of gunfire at the Haram Al-Sharif.
The sacred site is revered by both Muslims and Jews, known respectively as the Noble Sanctuary and the Temple Mount.
Israeli police occasionally restrict Muslim men under a certain age from entering partitions of the site, citing security concerns.
However, the police managed to find them, and in the shootout all three were killed.
Security forces locked down parts of Jerusalem's Old City including Al-Aqsa mosque on Saturday after an attack that killed two police officers escalated Israeli-Palestinian rift.
"It is time for the Arab leadership in Israel, and even outside it, to express a clear position against this criminal attack", the president said in a statement.
"We hold the Israeli government responsible for the changes they have made in the al-Aqsa Mosque and taking its control away from us".
"I condemn this attack as a cruel act in a place that is holy to many people".
The assault happened near a gate of Jerusalem's Old City - and the shooters then fled toward a mosque at the nearby holy site. Clashes erupted between the Israeli police and worshippers and several youth were arrested after being assaulted with batons and tear gas canisters.