The meeting is to be held at 5:00 p.m. (2100 GMT) at the formal request of Belgium and following a push led by France and Germany to place it on the agenda.
Britain also joined the European push for the talks, diplomats told AFP, adding that a joint declaration could be issued at its conclusion – either by the entire council or its European members if a full consensus cannot be reached.
The clashes come in the middle of the annual UN General Assembly and raise fears of a war between Azerbaijan and Armenia in the Caucasus.
The two countries have been locked in a territorial dispute over the Nagorno-Karabakh region for decades, with deadly fighting flaring up earlier this year and in 2016.
Officials in Nagorno-Karabakh region announced on Monday that 28 Armenian troops had been killed in clashes with Azerbaijani forces, bringing their military death toll to 59.
"Twenty-eight servicemen died in action,” Karabakh's Defense Ministry said in a statement, adding that the total death toll rose to 68, including nine civilian deaths — seven in Azerbaijan and two on the Armenian side.
Azerbaijan has not yet released information on military casualties since the latest fighting broke out.
The fresh flare-up is due to the failure of diplomatic negotiations within the framework of the Organization for Security and Cooperation in Europe (OSCE) Minsk Group, led by France, the US and Russia.
The key sticking point is Azerbaijan's demand that Armenia withdraw its military forces from Karabakh and let Azeris return to their homes, while Yerevan is apparently satisfied with the stalemate because it allows the status quo to continue.
Karabakh is internationally recognized as part of Azerbaijan, but it has an Armenian population because ethnic Azeris fled the territory in 1992 when separatists seized it in a move supported by Yerevan after the collapse of the Soviet Union.