On Saturday Israel sent extra troops into the occupied West Bank and its police broke up a crowd of stone-throwing Palestinians in Jerusalem.
Abbas called the measures "falsely presented as a security measure to take control over Al-Aqsa mosque".
He adds that he wants to see the Israeli military ceasing all incursions into Palestinian cities.
Three Jewish settlers were also killed in an alleged Palestinian attack in a settlement in the West Bank.
Jerusalem's top Muslim cleric, Mohammed Hussein, said protests would continue until the metal detectors are removed from the site, which is known to Muslims as the Noble Sanctuary and to Jews as the Temple Mount.
On Friday, fearing a mass demonstration, Israel barred access to all men under the age of 50 and buses carrying Muslim worshippers were prevented from entering Jerusalem, elevating already rising tensions.
Egyptian diplomats told Egypt's state-run news agency MENA on Saturday that the goal of the meeting is to discuss "calls for de-escalation amid ongoing clashes between Israeli forces and Palestinian protesters in East Jerusalem".
The decision to install metal detectors came after two border police officers were killed in an attack at the site last Friday.
The Palestinian was stopped by a neighbour, an off-duty Israeli soldier, who shot him, the official said. In a statement released on Sunday morning, the Islamic authorities in Jerusalem rejected the imposition of any new security measures at all at the site. On Friday, three Palestinians were killed and hundreds of others were wounded in violent clashes with Israeli forces.
The compound is considered the third holiest site in Islam and the most sacred for Jews, who call it Temple Mount.
The Palestinian Red Crescent said that two people were injured there and brought to the hospital for treatment.