The meeting was requested by Jordan in response to the latest deadly violence between Palestinians and Israeli security forces in Jerusalem and the West Bank in the past week.
In spite of the murders of the two policemen which made the additional security necessary, Palestinians believe the new gates violate agreed arrangements for entry to the mosque, Islam's third-holiest site.
Earlier, Palestinian worshippers and Israeli Police clashed outside the Old City of Jerusalem amid tensions over the Israeli authorities' decision to bar male worshippers under 50 from entering the area for Friday prayers.
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Israel installed metal detectors at the entrance of a holy site, prompting an outcry from Muslim worshipers and an uptick in violence.
Livni said the Israeli Cabinet now needs to show leadership to prevent the scenario from happening.
Three Israelis were also killed when a Palestinian snuck into a house in a West Bank settlement and stabbed them.
Sweden's Deputy U.N. Ambassador Carl Skau posted on Twitter after the meeting that Security Council members "agree on need for de-escalation, condemnation of violence and urgent dialogue to calm tensions in Jerusalem".
The site, which is sacred to Muslims, is also revered by Jews and known to them as Temple Mount.
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On Friday, Arab neighborhoods around the Old City of Jerusalem became the scene of clashes between Israeli police and Muslims, which gathered near the Old City to go to the Temple Mount and pray in Al-Aqsa mosque.
Israel's police reopened the mosque two days later, after installing metal detectors and surveillance cameras at the entrance of the Al-Aqsa mosque compound.
Palestinian president Mahmud Abbas says he is freezing contacts with Israel.
"I declare on behalf of the Palestinian leadership the suspension of all contacts with the occupation state (Israel) on all levels until Israel cancels its measures against our Palestinian nation in general and against Jerusalem and at Al-Aqsa mosque in specific", said Abbas.
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