Israeli security forces shot dead a Palestinian in the West Bank town of Nabi Saleh early on Sunday.
Hamas, the Islamic 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.
A family member says Israeli police have detained the top Muslim cleric in Jerusalem following a deadly Palestinian shooting attack from inside a major holy site.
Protesting the installation of metal detectors and cameras on the holy site, worshippers resorted to praying outside the compound, amid chants of "Allahu Akbar", or "God is Greatest".
Palestinian President Mahmud Abbas and Israeli Prime Minister Benjamin Netanyahu spoke by phone later as tensions rose over the attack and its aftermath.
This led Israeli security forces to close Jerusalem's holiest site for Jews and Muslims, sparking outrage as Muslims meant to worship there on their holy day, Friday.
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With the end of 2015 in Israel recorded a spate of attacks on Israelis by Palestinians and Israeli Arabs.
Arnon Segal, a Makor Rishon reporter and Temple Mount activist wrote on his Facebook page, "We're back, thank God".
The attack took place near the al-Aqsa mosque compound, also known as the Temple Mount or Haram al-Sharif, in Jerusalem's Old City. "It is incompatible with achieving peace and we must condemn it in the strongest terms, defeat it, and eradicate it". Temple Mount reopened after three suspects killed two police officers on Friday.
Spokeswoman Luba Samri said the attack happened Friday near a gate of Jerusalem's Old City and the shooters then fled toward a mosque at the nearby holy site.
Jews are allowed to visit, but are banned from praying there to avoid provoking tensions.
Al Jazeera reported that following the incident, Israeli police cleared the Al-Aqsa Mosque and closed it to the public.