The meeting will be held at 5:00 pm (2100 GMT), diplomats said. Belgium formally requested the session, after France and Germany had led a push for it to be placed on the agenda.
As early as Sunday, Estonia - a non-permanent council member - emphasised the need for such talks about the outbreak of deadly violence in the separatist region.
Britain also joined the European push for the talks, said diplomats, who added 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 raises fears of a war between ex-Soviet republics Azerbaijan and Armenia in the Caucasus.
Read also: Armenia and Azerbaijan: a decades-long bloody rivalry
Armenia and Azerbaijan have been locked in a territorial dispute over the ethnic Armenian region of Nagorny Karabakh for decades, with deadly fighting flaring up earlier this year and in 2016.
Increasingly deadly fighting raged Monday between Azerbaijani and Armenian forces, sparking bellicose rhetoric from Turkey despite international pleas for a halt in fighting between the longtime enemies.
Russia has a military alliance with Armenia, while Turkey backs Azerbaijan.
At least 95 people have been killed in the most recent fighting, including 11 civilians, according to the latest available tallies.