Kuwait called for the session after more than 50 Palestinians were killed by Israeli fire amid mass protests Monday, AP reported.
It was the deadliest day in Gaza since a 2014 cross-border war.
The Palestinian UN envoy wants the Security Council to condemn the killings.
It is not immediately clear what will come out of the discussion. At an emergency meeting after similar protests in March, council members urged restraint on both sides but did not decide on any action or joint message.
The Gaza Health Ministry said the Palestinian death toll in Gaza border protests has risen to 58, including 57 people killed by Israeli army fire and a baby who died from tear gas inhalation.
The ministry said six of those killed by gunshots were minors.
It said more than 2,700 people were injured Monday, including 1,360 by live fire. Of the wounded, 130 are in serious or critical condition.
On Monday, tens of thousands of Palestinians rallied near Israel's border fence to protest a blockade of their territory and the move of the US Embassy from Tel Aviv to Jerusalem (al-Quds) that day.