An Israeli police spokesman called the three assailants terrorists and said they were targeting police units in the areas.
It was gradually reopened on Sunday afternoon, making it the first time Friday prayer was not allowed at Al-Aqsa Mosque since 1969.
Israel's police chief says the attackers used weapons stored inside the compound and opened deadly fire on a police patrol.
Israel annexed East Jerusalem, where the Old City and the holy sites are located, following the 1967 Six-Day War and now claims sovereignty over the entire city - a move that is not recognised by the global community. They were pursued back to the shrine and shot dead, the BBC reported.
The temple was closed for the first time in almost 50 years on a Friday, Islam's holy day.
The Trump Administration condemned the terror attack on the Temple Mount and backed Israel's decision to temporarily close the holy site to Muslim worshippers.
Two officers killed in Friday's attack were neamed as Haiel Sitawe, 30 and Sergeant Master Kamil Shnaan, 22, both of whom were from Druze villages in northern Israel.More news: Froome defies wheel drama to retain Tour de France lead
The closing of the Temple Mount is an explosive measure on its own, however.
Dozens of Palestinian worshippers Monday prayed in the alleys of the Old City of Jerusalem leading to Al Aqsa Mosque after they refused to enter the Muslim holy place going through metal detector gates recently placed at the mosque entrances by Israeli police. Only Muslim residents of Jerusalem were allowed to enter.
"A chase ensued and the three terrorists were killed by police".
Abbas Zaki, of the central committee of al-Fatah, said Israel was morally responsible for the Jerusalem attack.
The PA president rarely condemns attacks on Israelis.
The Palestinian victims were identified as Muhammad Ahmad Muhammad Jabarin, 29, Muhammad Hamid Abd al-Latif Jabarin, 19, and Muhammad Ahmad Mufdal Jabarin, 19.
In September 2000, Israel's then-opposition leader Ariel Sharon made a provocative visit to the site, sparking Palestinian protests that quickly escalated into armed clashes between Palestinian gunmen and Israeli soldiers.
"We reject the changes imposed by the Israeli government", Sheikh Omar Kiswani, Al-Aqsa director, told reporters outside.