The Doha-based media network responded on Thursday, hours after the Israeli leader posted defamatory comments about the outlet's coverage to his Facebook page, saying Al Jazeera journalists "incite violence".
"The Al Jazeera network won't stop stoking violence over the Mount".
Al Jazeera, which has always been accused of being bias against Israel, has alongside other media been covering the al-Aqsa crisis the past couple of weeks.
Israeli Prime Minister Benjamin Netanyahu said Wednesday he will prepare legislation needed to shut down the Qatari-funded Al Jazeera television channel over its coverage of a dispute over a holy site in East Jerusalem.
Israeli authorities closed the Al-Aqsa Mosque that is venerated by Muslims and Jews - who call the site Temple Mount - and canceled weekly Friday prayers for the first time in almost five decades, following a deadly shootout July 14. There were put in place following a July 14 terror attack in which three terrorists shot two Israeli policemen to death with weapons they had smuggled onto the compound.More news: Lukaku aims to become 'complete package' at Man United
On Tuesday, Israel removed the metal detectors and planned on replacing them with less obtrusive surveillance. "If this does not happen because of legal reasons, I will work to legislate the laws required to remove Al Jazeera from Israel". The increased security methods, which are a staple at other Muslim holy sites across the region, sparked claims that Israel was inappropriately encroaching on the holy site. After a two-day shut-down of the compound, the Israeli state constructed metal detectors and cameras at the entrances.
Defense Minister Avigdor Liberman said at the time that the diplomatic isolation of Qatar had provided Israel with an "opportunity" to get rid of al-Jazeera and win points with potential Gulf allies.
A number of Arab countries have recently shut down their local al-Jazeera offices amid an ongoing spat with Qatar but Israel, which often touts its press freedoms, has allowed the station to continue operating.
However, Saudi Arabia and Jordan have both shut down Al-Jazeera offices in their countries.