Police have filed a request with Israeli courts for an order to re-close the building, but the court has reportedly delayed any decision to allow for more negotiations.
Monday's incident comes a day after Public Security Minister Gilad Erdan vowed that there will be "no second mosque on the Temple Mount" and that "God willing" Jews will be able to pray there freely in the near future.
There were no injuries reported from the attack.
Firas Dibs, spokesman for the Waqf, the Jordanian-appointed Islamic body that administers the site, said police had cleared almost all worshippers from the compound.
Dozens of police flooded the Temple Mount after the attack and clashed with Muslim worshippers.
The office of PA leader Mahmoud Abbas issued a statement Tuesday afternoon condemning the "dangerous Israeli escalation in the blessed Al-Aqsa Mosque" - a reference to the entire span of the Temple Mount compound - and calling on the global community to urgently intervene to force Israel to reopen the site after an Arab terror attack earlier in the day on the Israel Police station in the compound.
Palestinian political groups said escalating tensions around Al-Aqsa Mosque, the third holiest site in Islam, is a continuation of arbitrary policies of Israel against Palestinians.
Hatem Moussa Islamic Jihad Claims to Have Missiles That Can Reach Tel Aviv Jerusalem & Netanya'Destroy Zionist Regime
Bassem Abu Labda, an official from the Jerusalem Islamic Waqf which administers the site at the behest of the Jordanian monarchy, told The Times of Israel that mosque authorities "did not see any Molotov cocktail thrown at the police. Israel must reopen the mosque immediately".
The Israelis then shut the compound's gates and prevented Palestinians from entering the Old City through the Damascus Gate, a major entrance to the ancient walled area.
Palestinian Authority President Mahmoud Abbas' office condemned "the unsafe Israeli escalation in the blessed Al-Aqsa Mosque" and urged the worldwide community to intervene after the shutdown.
Police officers detain a Palestinian man outside the Old City of Jerusalem on March 12, 2019.
Saif said incidents in Jerusalem was as a result of silence of the worldwide community before the violation of all global agreements and human rights.
Jordanian officials reportedly suggested closing the Bab al-Rahma building for an indefinite period while it undergoes renovations. The area was closed in 2003 after allegations that the group overseeing the site was linked to terror activity.
Videos circulated on social media show Israeli forces arresting several protesters and violently attacking women.
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