Two police officers seriously injured in the attack succumbed while a third policeman has been slightly injured, according to police.
Police say the assailants used a knife, a pistol and two homemade machine guns.
An Israeli ambulance service said three men suffered gunshot wounds during the attack.
Police identified them as Muhammad Ahmad Muhammad Jabareen, 29; Muhammad Hamed Abdel Latif Jabareen, 19; and Muhammad Ahmad Mafadal Jabareen, 29.
The Palestinian Dar al-Ifta, an institute within the Palestinian Authority that issues religious edicts, condemned the arrest. Kamil Shnaan, 22, was the son of a former Israeli parliamentarian.
Israeli police said they had no comment.
"There is no justifiable excuse to prevent Muslims from praying at a holy place like the Al-Aqsa mosque", Görmez wrote on his official Twitter account.
Hamas, the Islamist movement that runs the Gaza Strip, called the attack "a natural response to the Zionist terrorism and the desecration of the Al Aqsa mosque", referring to previous Israeli raids at the site.More news: Rodgers takes lead at John Deere Classic
Mr Alsheikh said such an attack is "without precedent" at the holy site and an "incident of the highest severity". The compound was then declared closed and prayer was banned.
Hussein was later detained and taken into custody after he began to lead prayers out in the streets nearby.
Netanyahu also said he would preserve the status quo at the site, allaying Muslim concerns over their future access to the holy grounds.
Israeli border police officers stand guard at the entrance to the Al-Aqsa Mosque compound.
"This incident has the potential to ignite further violence".
Hussein called the closure "an escalation and aggression against al-Aqsa", the Arab-language name of the compound.
The Palestinian preacher described the Israeli measures in Jerusalem's Old City as a "collective punishment".
It lies in east Jerusalem, occupied by Israel in the 1967 Six-Day War and later annexed in a move never recognised by the worldwide community.
Jordan is a controlling force over the Waqf, the Mount's Islamic custodians. The picture was taken on June 7th, 1967, when the peak was this brigade's command post at the height of the Six-Day War, or Arab-Israeli War.
Forty Israelis, two American tourists and a British student have been killed in stabbings, shootings and car-rammings.
Rabbi Yaakov Kermaier, the president of Yakir - an Israeli community development organization focused on Druze-Jewish relations - told The Algemeiner that he had spoken with Druze leaders after the attack to tell them that "Jews around the world share their grief and pain today".