Israeli authorities reopened the compound to Muslims on Sunday, and non-Muslims on Monday, but with extra security measures, such as metal detectors.
Israeli security forces pursued and killed the three attackers and the compound was temporarily closed until Sunday.
Tensions have soared since Friday.
Palestinians subsequently rioted in Jerusalem, clashing with Israeli security forces near the Old City's Lion's Gate entrance.
At least four paramedics were injured, and 15 others were hit by rubber bullets, the charity said.
In an interview with Asharq Al-Awsat, Sheikh Hussein called on all Palestinians to boycott those procedures and preferred that Muslims pray in the streets and corridors of Jerusalem rather than to enter Al-Aqsa in a humiliating way. They argue that abiding by the new security measures will reinforce Israel's questioned sovereignty claim over the area.
The U.S.is working to help solve the dispute over Israel putting metal detectors at the entrance of the historic Al-Aqsa Mosque in the wake of a deadly shootout last week, a senior Palestinian official said Wednesday.
Omar Kiswani, director of al-Aqsa Mosque, told reporters outside the site that "the closure, the occupation, and the prevention of the call for prayers are all unfair and unjust and constitute a violation of the United Nations resolutions and the global agreements".
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Safadi said that Jordan, under the leadership of His Majesty King Abdullah the custodian of the holy Islamic and Christian sites in Jerusalem, will work with partners and friends to restore calm and resolve the crisis. The mosque is Islam's third holiest site after Mecca and Medina in Saudi Arabia.
The activists also ignore that metal detectors have been in place for years for Jewish and Christian worshipers accessing the Western Wall. Palestinians say the Israeli measures are aimed at paving the way for the Judaization of the city.
Maybe Israeli metal detectors wouldn't stop Islamic prayers if these prayers didn't seem to involve shooting and stabbing non-Muslims.
Israeli Prime Minister Benjamin Netanyahu took the decision to install the metal detectors and cameras following a meeting with security officials on Saturday.
"What is happening is gross aggression and a risky Israeli plan. that will increase tensions in Jerusalem specifically and the region generally, explode the situation, and ignite a religious war", he said.