Libya circulated a draft statement to council members expressing "serious concern at the escalation of the situation in Gaza" and calling on Israel and Hamas "to stop immediately all military activities."
The 15-member council then held emergency consultations behind closed doors late on Sunday to discuss the proposed presidential statement, which would also call for all parties "to address the serious humanitarian and economic needs in Gaza." Steps would include reopening border crossings.
"We need to have from the Security Council reaction tonight to bring this latest addition of aggression against our people in Gaza to an immediate halt," said Riyad Mansour, a Palestinian UN observer.
He said 3,000 Palestinians have been killed and injured since Israeli warplanes starting bombing Gaza a week ago, and if the ground offensive "is not stopped immediately
then we will have perhaps thousands more of Palestinian civilians killed and injured."
"This is immoral. This is illegal. This is unacceptable and the Security Council cannot continue to sit on its hands," Mansour said. "The Security Council has to bring Israel into compliance and to stop this aggression immediately."
With more than 480 Palestinians killed in Gaza, and just four killed in Israel, the Israeli government has come under strong criticism for the excessive use of force.
Meanwhile, UN chief Ban Ki-moon reiterated his call for an immediate cease-fire and urged regional and international partners "to exert all possible influence to bring about an immediate end to the bloodshed and suffering," the statement said.
The secretary-general said the Israeli ground operation is complicating efforts by the Quartet of Mideast peacemakers to end the violence.