In a closed-door meeting of the council, Palestine's UN ambassador Riyad Mansour said Israel is "vulgarly and publicly boasting about its willful killing of Palestinians" after an air strike killed Hamas mastermind Ahmed Jabari.
Israel, which said the airstrikes were launched in response to days of rocket fire out of Hamas-ruled Gaza, was expected to speak in the meeting.
Israel's ambassador Ron Prosor said earlier that no one complained when Palestinians were raining rockets on Israeli civilians, and said no nation would tolerate that.
In the text of his statement Mansour said: "War crimes are being perpetrated by Israel against the Palestinian people."
"The international community must act to bring to bring an end to Israel's illegal policies and practices against the Palestinian people."
US defends Israel
US ambassador Susan Rice was attending the meeting. An AFP report said Rice strongly defended Israel's military riposte to "vicious" Hamas attacks late on Wednesday.
While Arab envoys called on the council to condemn Israel's attacks, Rice said: "There is no justification for the violence that Hamas and other terrorist organisations are employing against the people of Israel."
Secretary general Ban Ki-moon released statements saying he had spoken to Egyptian President Mohamed Morsi about "the worrisome escalation of violence in southern Israel and Gaza and the need to prevent any further deterioration."
He also said he had talked to Israeli Prime Minister Benjamin Netanyahu to express concern about "an alarming escalation of indiscriminate rocket fire from Gaza into Israel and the targeted killing by Israel of a Hamas military operative in Gaza". – Sapa-AFP