The chief of Russia's general staff, Valery Gerasimov, told President Vladimir Putin on Wednesday that a Ukrainian offensive in Russia's Kursk region had been halted.
In televised comments, Gerasimov said Russian forces were continuing to "destroy the enemy" in areas near the border.
Earlier on Wednesday, Russia said that it was fighting intense battles against Ukrainian forces which had penetrated the Kursk region in one of the largest incursions into Russia since the Ukraine war began in February 2022.
Russia has advanced this year after the failure of Ukraine's 2023 counteroffensive to achieve any major gains, and has taken 420 sq km (162 sq miles) of territory from Ukrainian forces since June 14, Sergei Shoigu, head of Russia's security council, has said.
Ukraine struck back on Tuesday - and the battles continued through the night into Wednesday as Ukrainian forces pushed to the northwest of the border town of Sudzha, 530 km (330 miles) southwest of Moscow, Russia's defense ministry said.
"The Kyiv regime has launched another major provocation," President Vladimir Putin told members of the Russian government about the Kursk attack.
Putin said Ukrainian forces were firing "indiscriminately" at a range of civilian targets in the region and said that he would shortly have a meeting with top defense ministry and Federal Security Service officials.
Both Kyiv and Moscow say they do not target civilians in the war triggered by Russia's full-scale invasion.
Russian Telegram channels carried unverified footage of shelled houses. Alexei Smirnov, the acting governor of the Kursk region, said there were casualties but gave no exact toll and called on citizens to donate blood.
He said a Ukrainian attack drone had hit an ambulance outside the town, killing the driver and a paramedic and wounding a doctor.
Sudzha is the last operational trans-shipping point for Russian gas exports to Europe via Ukraine. Just 60 km away to the northeast is Russia's Kursk nuclear power station.
Ukraine has not commented on the events. Russia sent reserves to help shore up Russian defenses.
Crucial juncture
The battles around Sudzha come at a crucial juncture in the conflict, the biggest land war in Europe since World War Two. Ukraine is losing territory and Kyiv is deeply concerned that US support could drop off if Donald Trump wins the November election in the United States.
Trump has said he would end the war, so both Russia and Ukraine are keen to gain the strongest possible bargaining position on the battlefield while pinning down Russian forces and showing the West that it can still mount major battles.
Shoigu said on Tuesday that the window for peace was narrowing and that the longer it took for Kyiv to begin to talk about terms, the costlier the peace would be for the Ukrainian people.
Russian military bloggers reported intense battles and said Ukraine had penetrated about 10-15 km inside the Russian border.
The defence ministry said that it was continuing to fight Ukrainian units "in the areas of the Kursk region directly adjacent to the Russian-Ukrainian border."
It said the fighting was continuing, adding that Russian forces had destroyed Ukrainian armor, including seven tanks.
Forces describing themselves as voluntary paramilitaries fighting on Ukraine's side penetrated parts of the Belgorod and Kursk region this year, triggering a major push by Russian troops to carve out a buffer zone in Ukraine's northeast.