Israeli border police officers body-search Palestinians in Jerusalem's Old City.
Police say the assailants used a knife, a pistol and two homemade machine guns.
"The murderous terror attack at the Temple Mount was stopped by the courageous Israeli policemen who threw themselves in the way, and prevented an even greater disaster", said Rivlin in a statement communicated by his spokesman.
Netanyahu stressed that Friday's closure was for security reasons and did not represent a change in what is called the "status quo" agreement about the care, custody and access to the religious site.
Some witnesses said that Israeli forces entered the mosque compound with shoes on, which is highly disrespectful to the sacred space, and also proceeded to dump out garbage containers on the floor, claiming to be "searching" them.
The Muslim-administered site is revered by both Muslims and Jews.
The rare attack from within the contested shrine, known to Muslims as the Noble Sanctuary and to Jews as the Temple Mount, raises new concerns about an escalation of violence.
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Toronto- Closed since Friday morning following the shooting deaths of five people, the Al-Aqsa mosque in Jerusalem's Old City has become the focal point of rising tensions between Israelis and Palestinians.
The fighting inside the complex was one of the worst incidents of violence on the Temple Mount in years.
One unnamed Israeli official responded to the Jordanian statement, telling Israeli TV that "instead of condemning the attack, Jordan chose to attack Israel, which is protecting worshipers and maintaining freedom of worship in the place".
Three Palestinians and two Israeli policemen died on Friday following a clash between security forces and citizens in Jerusalem's Old City.
The grand mufti of the city, Mohammed Hussein, was detained for questioning Friday at a police station in the Old City, his son, Omar, told The Associated Press.
In the past two years, Palestinian assailants have killed 45 Israelis, two Americans and a British tourist in various attacks involving stabbings, shootings and vehicle crashes.
The site has been a flashpoint for violence in the past, with friction there sparking major rounds of Israeli-Palestinian violence. It later annexed the city in 1980, claiming all of Jerusalem as the Jewish state's "eternal" capital - a move never recognized by the global community. Waqf officials said Israeli police detained its guards there after the attack.