The urgent talks were requested by council member Jordan following a meeting on Thursday of Arab ambassadors who expressed alarm at the escalating situation.
UN Secretary-General Ban Ki-moon has repeatedly called for calm following weeks of violence that have left at least 30 Palestinians dead.
Read: Three dead as Jerusalem sees bloodiest day in rising unrest
Palestinian envoy Riyad Mansour told reporters that the situation was "very explosive" and called on the Security Council to "shoulder its responsibility" with action to quell the violence.
Israeli security forces deployed massively in Jerusalem Thursday as Jews armed themselves with everything from guns to broomsticks.
The uptick in violence has raised fears that a third Palestinian intifada, or uprising, might erupt.
The Security Council meeting is scheduled for 11:00 am (1500 GMT).
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