Aharonovich was quoted by Israeli radio as saying that he would not hesitate to close the site to Muslim worshippers in light of recent "disturbances," noting that it had been closed to Jewish visitors on Sunday.
But, he added, it was up to Jerusalem police to take such a decision.
Earlier Monday, Deputy Knesset Speaker Moshe Feiglin – under heavy Israeli police protection – had forced his way into the Al-Aqsa compound.
The intrusion came amid clashes between Muslim youth and Israeli police, the latter of which stormed the holy site in the early hours of the morning and tried to forcibly evict Palestinian worshippers from the area, eyewitnesses said.
The clashes came only one day after Feiglin had called for storming the Al-Aqsa Mosque Compound on Monday on the occasion of Sukkot, a weeklong Jewish pilgrimage festival that began last Wednesday.
In a statement posted on his website, Feiglin called on Jews to converge outside the mosque compound at 6:30am on Monday before storming the site.
Source: World Bulletin