AGDAM, Azerbaijan — Overshadowed by the fighting in Ukraine, another armed conflict in the former Soviet Union — between Armenia and Azerbaijan over the territory of Nagorno-Karabakh — has escalated with deadly ferocity in recent months, killing dozens of soldiers on each side and pushing the countries perilously close to open war.

The month of January was heavily stained by blood, with repeated gun battles and volleys of artillery and rocket fire. Two Armenian soldiers were killed and several wounded in a fierce gunfight on Jan. 23 along the conflict’s northern front. That set off a weekend of violence including grenade and mortar attacks that killed at least three Azerbaijani soldiers.

The most recent clashes prompted an unusually pointed rebuke by international mediators who met on Monday in Krakow, Poland, with the Azerbaijani foreign minister, Elmar Mammadyarov.

“The rise in violence that began last year must stop,” the mediators, from France, Russia and the United States, said in a joint statement, adding, “We called on Azerbaijan to observe its commitments to a peaceful resolution of the conflict. We also called on Armenia to take all measures to reduce tensions.”