The militant Palestinian Islamist movement Hamas had called for a "day of rage" over al-Aqsa.
Palestinians have also been angered by Israeli plans that could allow police to open fire on stone-throwers.
An Israeli motorist died earlier in the week in an accident apparently caused by a rock-throwing attack in Jerusalem.
Several security incidents were reported on Friday:
At least two rockets were fired into Israel from the Palestinian territory of Gaza, with one damaging a bus
Israel responded with overnight air strikes on training camps belonging to Hamas in Gaza
In East Jerusalem, police said three border guards were injured by a fire bomb thrown at their vehicle
Also in East Jerusalem, a bus was attacked with stones and set ablaze
There were clashes in several places in the occupied West Bank, with the Red Crescent saying seven Palestinians suffered injuries from live fire
Thousands of Jordanians held a solidarity march in Amman
The al-Aqsa mosque compound itself was reported to be quiet on Friday. Israeli police set up checkpoints outside the site, limiting the age of worshippers to 40 and above for men.
The compound - known to Jews as the Temple Mount and to Muslims as al-Haram al-Sharif - is the holiest site in Judaism, and contains the al-Aqsa Mosque - the third holiest site in Islam.
Tensions have been running high in Jerusalem since Israel banned two Muslim groups which confront Jewish visitors to the compound.
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