The council will now meet at noon (1700 GMT) on Saturday to vote. The decision was made on Friday after the draft introduced by Qatar on behalf of Arab member states was softened to make it more palatable to Western countries.
Council members will now have time to consult their governments for instructions on how to vote.
The amended draft no longer refers to the death of 18 Palestinians, mostly women and children, during the Israeli shelling of Beit Hanoun as "a massacre".
A call for the deployment of UN observers to supervise a ceasefire in the Gaza Strip has also been removed.
The new text would condemn Israel's military operations in Gaza, particularly the Beit Hanoun incident along with "the firing of rockets from Gaza into Israel".
It calls on Israel "to immediately cease its military operations that endanger the Palestinian civilian population in the Occupied Palestinian territory, including East Jerusalem, and to immediately withdraw its forces from within the Gaza Strip to positions prior to June 28, 2006".
Diplomatic sources said the US
was expected to veto the draft
The text also calls for an "immediate halt of all acts of violence and military activities" by Israelis and Palestinians.
If the resolution is passed it will direct the UN secretary general to set up a fact-finding mission on the Beit Hanoun attack within 30 days.
Despite the changes, the US is expected to veto the draft.
Yehya al-Mahmasani, the Arab League ambassador to the UN, speaking to Al Jazeera said: "The United States has not suggested any amendments or remarks over the draft resolution. This is a bad sign indicating that it would vote against the resolution."
Britain, Denmark, Japan and Slovakia are expected to abstain, a diplomatic source told the AFP news agency.
Other diplomats said Arab countries would probably then take their case to the 192-member General Assembly, where it would get a more sympathetic hearing.
The Israeli strike has received widespread condemnation and prompted Mahmoud Abbas, the Palestinian president, to accuse Israel of destroying the chances for peace, and to declare three days of mourning in the Palestinian territories.
Israel has said the civilian deaths were caused by a "technical failure" by its military.