Both the Jews and Arabs claim it for religious significance.
Jerusalem's chief of police ordered the Temple Mount closed and evacuated, the Post reported.
The site includes the Al-Aqsa mosque and the Dome of the Rock.
Prime Minister Benjamin Netanyahu and top Israeli security brass decided Saturday night on new initial security arrangement for entry to the Temple Mount, in the wake of a deadly terrorist attack Friday that left two Border Guard Police officers dead and more wounded.
Bassam Al Halaq, a senior official of Awqaf, an Islamic authority in charge of Al-Aqsa, told Al Jazeera that the Israeli police were searching the entire compound, breaking through doors.
The fighting inside the complex was one of the worst incidents of violence on the Temple Mount in years.
"The Israeli government is ready to take it in that direction because it reiterates the negative stereotype of the aggressive Palestinian, especially under global silence over its breaches of human rights and worldwide law in Jerusalem", she added.
"Al Aqsa Mosque is closed for the first time since 1969 and no one responds to the decision".
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Jaffa Gate, heavily used by tourists and near the Old City's Jewish Quarter, was open but with a heavy police presence.
UN Secretary-General Antonio Guterres has warned the attack could spark more violence and urged all sides to avoid escalation.
Hussein was detained at the Lions Gate, the bodyguard said.
Gradually reopening the site to worshippers and visitors "will be based on an estimate that will be made Sunday", he said.
"The Israeli government continues to prohibit prayers and adhan (call for prayer) and ban preachers from entering the Al-Aqsa mosque", mosque preacher Sheikh Ekrima Sabri told Anadolu Agency.
The site is administered by the Islamic Waqf organisation.
From October 2015, Israel and the palestinian Territories are plagued by violence that caused the death of 281 Palestinians, 44 Israelis, two Americans, two Jordanians, an Eritrean, Sudanese and British, according to a count by the AFP. Israeli authorities then shut the compound down citing security concerns, just hours before Muslim Friday prayers.
Two soldiers were also killed, while two others were injured.