The ministry had sent reserves on Tuesday to help repel hundreds of Ukrainian fighters backed by tanks from Kursk, in a ground incursion shaping as one the largest into Russian territory during the war, now more than two years old.
The situation was "controllable", Alexei Smirnov, the acting governor of the southwestern Russian region, said in posts on the Telegram messaging app.
All emergency services were on "high alert", he said on Wednesday, calling for people to donate blood to replenish medical supplies.
The region was under a dozen air raid alerts over the past 24 hours, Smirnov's posts showed. By Wednesday morning, there were no reports of fresh ground fighting.
Five people were killed, including two ambulance crew, with at least 20 wounded, among them six children, in the fighting that erupted on Tuesday, Russian officials said.
Ukraine made no official comment, though there was evidence of some military action from its side of the border. Both Kyiv and Moscow say their attacks do not target civilians.
Ukraine regularly fires artillery and missiles into Russian territory and has hit targets deep inside Russia with long-range attack drones, but infantry raids are rare.
Forces describing themselves as voluntary paramilitaries fighting on Ukraine's side inflicted minimal damage in a major incursion into parts of Belgorod and Kursk region this year, but the purpose of the raids remains unclear.
On Tuesday, Ukraine's general staff made no mention of any Ukrainian offensive operation inside Russia.
Moscow says Ukrainian fighters, backed by tanks, had attacked border units. (AP PHOTO)
Official Russian social media accounts said up to 300 Ukrainian fighters, backed by tanks, had attacked border units in two localities in Kursk - Nikolayevo-Daryino and Oleshnya.
Reuters was unable to verify the battlefield accounts of either side.
Officials said the border town of Sudzha had also come under assault and Smirnov said a Ukrainian attack drone had hit an ambulance outside the town, killing the driver and a paramedic and wounding a doctor.
A senior Orthodox clergyman said Ukrainian shelling had set ablaze a cathedral and other buildings within a large monastery outside Sudzha, but no one was hurt.
Kursk region is also the site of the Kursk Nuclear Power Plant, but Smirnov said the facility was operating without incident.
Russia's air defence systems destroyed also three drones that Ukraine launched at Belgorod region and two each over the Voronezh and Rostov regions, the defence ministry said.
In the Voronezh region - several hundred kilometres south of Moscow - the drones damaged several residential buildings and cars, the regions' governor said on Telegram.
Ukraine's main military effort is focused on pushing back Russian military forces who control nearly a fifth of its territory. Russian troops have made a series of gradual gains in the past six months.
