The request followed a letter from Palestinian representative to the United Nations Riyadh Mansour calling for a urgent meeting to "address this crisis situation in occupied east Jerusalem."
Jordan, a Security Council member, put forward the request late Monday and was awaiting a response from Argentina, which chairs the 15-member council, on setting a date.
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Diplomats told AFP the meeting was unlikely to be held on Tuesday or Wednesday.
Israel pledged to build more than 1,000 new settler homes in east Jerusalem on Monday, angering Palestinians who warned it could trigger an "explosion" of violence.
In his letter, the Palestinian representative called on the council to demand that Israel rescind its plan immediately and "commit to the path of peace that it has clearly and recklessly abandoned."