Israel assassinated quadriplegic Hamas spiritual leader and founder Shaikh Ahmad Yasin, outside a mosque in the occupied Gaza Strip on Monday.
The killing has been criticised around the world as an escalation of Middle East violence.
Algeria, the only Arab nation on the 15-member council, introduced a draft resolution late on Wednesday condemning "the most recent extrajudicial execution committed by Israel". It has scheduled a vote late on Thursday.
The measure also condemns "all attacks against any civilians as well as all acts of violence and destruction" in an effort to get European votes.
The United States, Israel's staunch ally, has only said it is troubled by the assassination.
It categorically opposes the draft resolution because it does not mention Hamas as a group responsible for attacks against Israel.
Hamas is spearheading the Intifada or uprising in an effort to end Israel’s occupation.
The United States, Britain, France, Russia and China are permanent Security Council members with veto rights.
Minimum of nine
If a council resolution receives the minimum nine votes needed for adoption and is vetoed, the sponsors can call an emergency session of the 191-nation General Assembly, where a measure critical of Israel is bound to be adopted.
Assembly resolutions, compared to those passed by the Security Council are not binding, except on issues such as UN budgets, but express the will of nations around the world.
Reaching nine votes depends in part on the four European Union members and their allies in the Security Council.
The United States, Russia, the European Union as well as the United Nations are members of a so-called quartet of Middle East advisers but have rarely had a unified position on the issue in the Security Council.