Muslim worshippers were very angry with the incident and wanted to reopen the site immediately.Palestinian religious and political leaders, Jordan and the Organization of Islamic Cooperation, a world Islamic body, among others been called to reopen it as soon as possible.
The temple was closed for the first time in almost 50 years on a Friday, Islam's holy day.
Israeli authorities shut the area after the attacks - the most serious incident in years close to the highly sensitive compound, which is holy to both Muslims and Jews.
The two policemen killed were Israeli Arab citizens from the country's Druze community.More news: Britain and European Union 'get to work' on fresh Brexit talks
The Al Aqsa mosque compound in Jerusalem reopened on Sunday after being closed following a deadly attack, but some Muslims were refusing to enter because of new Israeli security measures, including metal detectors and cameras.
The Palestinian victims were identified as Muhammad Ahmad Muhammad Jabarin, 29, Muhammad Hamid Abd al-Latif Jabarin, 19, and Muhammad Ahmad Mufdal Jabarin, 19.
The early morning attack was carried by three Arab-Israelis from the town of Umm al-Fahm in northern Israel.
Mahmoud Abbas condemned the attack on the Temple Mount, the official PA media agency Wafa reported. "It is incompatible with achieving peace and we must condemn it in the strongest terms, defeat it, and eradicate it".
"We hold the Israeli government responsible for the changes they have made in the al-Aqsa Mosque and taking its control away from us".
The new step led to bigger disputes and a war on "the sovereignty of the mosque", leading to further confrontations near one of the gates, and leaving several Palestinians injured.