France and Britain called for the meeting as Russia said a new ceasefire in Aleppo could be announced within hours.
French Ambassador Francois Delattre described Aleppo as the "martyred center of the resistance" to Syrian leader Bashar al-Assad and compared the city to besieged Sarajevo during the Bosnian war.
"Aleppo is burning and it is crucial that we focus on this top priority issue," said British Ambassador Matthew Rycroft.
The 15-member council will hear a report from the UN's top political affairs official Jeffrey Feltman on the situation in Aleppo, where fresh fighting including a rocket attack on a maternity hospital left 19 dead on Tuesday.
"I am hoping that in the near future, maybe even in the next few hours, such a decision will be announced," Lavrov said after meeting UN Syria envoy Staffan de Mistura in Moscow.
A surge of violence that erupted on April 22 has left more than 270 people dead in the divided northern city and undermined efforts to revive peace negotiations.
After a relative lull in clashes on Monday and early Tuesday, rebels in eastern Aleppo fired a barrage of at least 65 rockets into government-controlled neighbourhoods, Syrian state news agency SANA reported.
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