The draft resolution backed by Arab countries calls for a lasting ceasefire between Hamas and Israel, as well as an international effort to rebuild Gaza after four weeks of fighting killed at least 1,867 Palestinians and 67 Israelis.
"We are in consultation with all the Council members and hope that in the next day or two we can come up with a product," Jordanian Ambassador Dina Kawar said.
The latest initiative came as a 72-hour truce appeared to be holding and the two sides agreed to send envoys to Cairo for peace talks.
The 15-member Council has adopted a statement calling for a ceasefire, but the Palestinians and Arab countries have said it falls short of a formal resolution from the top body.
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Agreement on the statement was reached after the United States dropped reservations that the wording would single out Israel for harsh criticism.
The new text, revised from a previous version circulated by Jordan two weeks ago, calls for a full UN investigation of the attacks on UN-run schools in Gaza, used as shelters for civilians fleeing the fighting.
Britain, which holds the Security Council presidency this month, said talks would continue over the coming days on the proposed resolution but that the outcome would depend on the situation on the ground.
"Perhaps the situation is a bit different and we need a slightly different approach in the Security Council," said Ambassador Mark Lyall Grant.