"Since the start of active hostilities, Russian peacekeepers have evacuated the civilian population from the Mardakert, Martuni and Askeran districts," the ministry said in a statement.
"Some 5,000 people have been brought to the location of the peacekeeping contingent."
All evacuees are being provided with resting places and hot meals, and Russian military medics are providing them with medical treatment, the statement said.
The ministry said Russian peacekeepers continue to fulfill their tasks in the region and maintain "continuous interaction with Baku, Yerevan and [the Karabakh city of] Stepanakert aimed at preventing bloodshed, ensuring security and compliance with the norms of humanitarian law with regard to civilians, as well as ensuring the safety of the Russian peacekeeping contingent."
The ministry recalled that an agreement was reached on Wednesday with the parties to the conflict, with the mediation of the command of the Russian peacekeeping contingent, to cease fire completely in the region. The situation is being monitored around the clock, the ministry added.
Hostilities earlier broke out between Armenia and Azerbaijan after Baku began an "anti-terrorist operation" to "restore constitutional order" in Nagorno-Karabakh, a development that Yerevan condemned as an act of aggression as it had no military presence in the disputed region. Azerbaijan had earlier indicated it was only targeting military objects in the area.
Military hostilities previously broke out in the region in 1992 and in 2020; however, until recently both Armenia and Azerbaijan were on the verge of of cementing a peace agreement by the end of the year after Armenian Prime Minister Nikol Pashinyan declared Yerevan was ready to recognize Azerbaijan's sovereignty within its Soviet-era borders, including Karabakh. Azerbaijani leader Ilham Aliyev later indicated that both nations could sign a peace deal in the later half of the year so long as Yerevan did not change its stance.