Abbas was to also address the meeting after meeting Condoleezza Rice, the US secretary of state, earlier on Tuesday.
Al Jazeera's Ghida Fakhry, reporting from New York, said a draft resolution could be tabled by Libya, the only Arab member of the current security council, as early as Tuesday evening.
It could then be put to a council vote on Wednesday evening, although many ambassadors said this was unlikely, our correspondent said.
Last week, the US blocked a Libyan-backed proposal for the UN to call for an immediate ceasefire in Gaza.
The latest council meeting follows a flurry of diplomatic meetings on the crisis earlier on Tuesday and on Monday.