"The storming of al-Aqsa mosque compound by Israeli occupation forces this Eid morning is an act of recklessness and aggression", she said in a statement.
The Jewish holiday is traditionally marked by "an increase of Jewish visitors to the site", according to Al Jazeera.
"International justice is one-eyed and the justice that is not won through worldwide laws will be taken through the resilience and resistance of the peoples", Bassil went on to say.
Israeli media also reported the clashes, saying Palestinian worshippers were marking Eid Al-Adha "which coincides with" the so-called Jewish holiday of Tisha B'Av.
In a bid to ease tensions, police initially barred Jewish visits to the site on Sunday but Muslim worshippers still feared they would be allowed in and protested there.
In response to the calls, the Higher Islamic Commission (HIC) in East Jerusalem, the Council for Waqf and Islamic Affairs and the Council of Fatwa called on all mosques around the city of Jerusalem to close on Eid al-Adha, in order to allow more people to join Eid Al-Adha prayers at al-Aqsa mosque compound as a means "to protect the mosque" during the anticipated raid. Jews are also observing on Sunday the Ninth of Av, a day of fasting and mourning for the destruction of the two Biblical temples which stood at the site in antiquity. On Saturday, Israeli troops killed four Palestinian militants who attempted to cross the Gaza border fence.
Hanan Ashrawi, a senior official in the Palestine Liberation Organisation, accused Israel of provoking religious and political tension. The site is now home to the Dome of the Rock and the Al Aqsa Mosque, the third-holiest site in Islam.
After the confrontations died down, Jerusalem District Police Chief Doron Yedid said on Kan radio that he had lifted the ban.
Israel annexed East Jerusalem in the 1967 war and declared the entire city as its eternal indivisible capital in 1980, a move that has never been recognized by most of the worldwide community.
The reversal came after Israeli prime minister Benjamin Netanyahu's religious nationalist allies called for the site to be opened to Jewish visitors.
Israel occupied East Jerusalem during the 1967 Middle East war.