Police said that three armed assailants arrived at one of the gates to when they noticed policemen present.
Israeli security forces stand guard in Jerusalem's Old City after Friday's shooting attack.
The statement appeared stronger than previous such responses from Abbas, who has repeatedly called for non-violent resistance to Israel s occupation without specifically condemning Palestinian attacks.
MDA paramedics Israel Weingarten and Aharon Adler described the scene: "Near the Lions' Gate, police officers led us to 3 casualties from gunfire". Both were officers in the border police unit, and Satawi is survived by his wife and their three-week-old son, police say.
After the shooting, the police closed the entire compound of Al-Aqsa Mosque, and initiated extensive searches in the area "to ensure no weapons are in it".
The location at the holy site was also likely to lead to tensions. Israeli forces have killed more than 254 Palestinians in that time, with authorities describing most of the dead as attackers.
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The site is known to Jews as the Temple Mount and to Muslims as the Noble Sanctuary.
News agency Wafa said Palestinian President Mahmoud Abbas condemned the attack when speaking to Israeli Prime Minister Benjamin Netanyahu on the phone.
Jews revere the site, where the two Jewish temples stood in biblical times, as the Temple Mount.
The three Palestinian assailants are reportedly Arab-Israelis, 19, 19, and 29-years old. An Israeli police spokesman said the identities of the suspects had been put under gag order, as had information about the victims.
"It was chose to shutter the Temple Mount today for security reasons".
A wave of Palestinian street attacks that began in 2015 has slowed but not stopped.
"We are determined to reach the Al-Aqsa Mosque and to hold all prayers in it", he said".