Palestinian Authority President Mahmoud Abbas responded that there would be "grave repercussions" for what he called a "dangerous Israeli escalation" of violence.
There were no injuries reported from the attack.
The attack comes amid increased tension on the Temple Mount.
Tensions have been especially high since the Waqf Islamic authority, which operates the Muslim holy sites, breached the Gate of Mercy on the Mount last month.
Around the same time physical confrontations broke out between Israeli forces and Palestinians at the site.
The commander of the Jerusalem district, Major General Doron Yedid, arrived at the scene shortly after and ordered for the compound to remain closed in order to inspect the area for other explosive devices that might be left behind by the attackers.
Abbas said through his office he has been in touch with "relevant parties, including Jordan" to "pressure the occupation's government to halt this unsafe escalation".
In a statement cited by Haaretz, Hamas "called on Palestinians from all over - in Jerusalem, the West Bank and within the Green Line - to storm Al-Aqsa Mosque, to break the barricade that the Israeli police have thrown upon us, and to never give up on the right to enter the complex freely".
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Meanwhile Turkish Foreign Minister Mevlut Cavusoglu called on "the whole world to react to Israel's brazen attacks on our scared land".
The U.N. Mideast envoy, Nickolay Mladenov, urged both sides to "respect the status quo" at the holy esplanade and exercise restraint "to avoid inflaming an already tense situation".
After the incident, Israeli police sealed off entrances to the compound.
Officials in Jordan have confirmed that they are in negotiations with Israel to resolve the dispute.
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.
Jerusalem's Temple Mount erupted in violence Tuesday afternoon after a firebomb was thrown at a police post on the holy site.
But police quickly deployed across the hilltop compound, scuffling with Palestinians in the area as they searched for the assailants.
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.
A number of detentions were carried out by Israeli forces across the compound.