Diplomats said the meeting will be held behind closed doors.
"Sweden, France and Egypt request UN Security Council to urgently discuss how calls for de-escalation in Jerusalem can be supported," said Security Council coordinator of the mission of Sweden Carl Skau on his Twitter account on Saturday.
Three Israelis were killed on Friday in a stabbing attack by a Palestinian in a West Bank settlement.
The attack followed clashes between Palestinians and Israeli forces in Jerusalem's Old City, in which three Palestinians died.
In a statement released on Saturday, the Middle East Quartet -- Russia, the US, the European Union and the UN -- expressed concerns over the escalating tensions.
"The Quartet envoys reiterate that violence deepens mistrust and is fundamentally incompatible with achieving a peaceful resolution of the Israeli-Palestinian conflict," said the statement.