Russian and Ukrainian forces are engaged in heavy fighting around two towns in Ukraine's eastern Donbas region, while Kyiv came under attack from Russian drones early on Monday, officials said.
Fighting was intense this weekend in Donetsk and Luhansk, which make up the industrial Donbas, and the Kherson province in the south. They constitute three of the four regions Russia said it had annexed last month after holding what it called referendums – votes that were denounced by Kyiv and Western governments as illegal and coercive.
"The key hot spots in Donbas are Soledar and Bakhmut," Ukrainian President Volodymyr Zelenskiy said in his nightly address on Sunday. "Very heavy fighting is going on there."
Bakhmut has been a target of Russian forces in their slow move through the region since taking the twin industrial towns of Lysychansk and Sievierodonetsk in June and July. Soledar is just north of Bakhmut.
Russia's defence ministry said on Sunday its forces had repelled efforts by Ukrainian troops to advance in the Donetsk, Kherson and Mykolaiv regions. Russia also said it was continuing air strikes on military and energy targets in Ukraine.
Reuters was not able to independently verify the reports on the fighting.
Away from the front line, Ukraine's capital of Kyiv was attacked on Monday by so-called kamikaze drones, Andriy Yermak, head of the president's staff, wrote on the Telegram messaging service.
"Russians think it will help them," Yermak said.
Kyiv's Mayor Vitalii Klitschko said on Telegram that several blasts had rocked the central Shevchenkivskyi district of Kyiv, with a Reuters witness reporting three explosions.
The same district was hit by explosions a week ago, as Russia ordered the biggest aerial offensive against Ukrainian cities in retaliation for a blast on a bridge linking mainland Russia to Crimea - the peninsula Russia annexed from Ukraine in 2014.
Ukrainian military analyst Oleh Zhdanov suggested the heaviest fighting was occurring north of Bakhmut, asserting that Ukrainian forces had repelled Russian advances on the towns of Torske and Sprine in the past 24 hours.
"(The Russians) have decided to move through Torske and Sprine," Zhdanov posted online. "Positions in those places are changing hands regularly."
The head of the Russian-backed administration in the Donetsk region said on Sunday Ukrainian shelling had damaged the administration building in the regional capital.
"It was a direct hit, the building is seriously damaged. It is a miracle nobody was killed," said Alexei Kulemzin, surveying the wreckage, adding that all city services were still working.
There was no immediate reaction from Ukraine to the attack on Donetsk city, which was annexed by Russian-backed separatists in 2014 along with swathes of the Donbas.
Rybar, a pro-Russian military channel on Telegram, said Ukrainian forces again shelled the southwestern town of Belgorod, near Ukraine.
Anti-aircraft units intercepted most of the attacks, but there were two explosions near the airport. Three people were injured, it said.
In Russia, authorities said on Sunday, a criminal investigation had been opened after gunmen shot dead 11 people and wounded 15 at a military training ground in the Belgorod region.
Russia's RIA news agency, citing the defence ministry, said two gunmen opened fire with small arms during a training exercise on Saturday, targeting personnel who had volunteered to fight in Ukraine. RIA said the gunmen, who it referred to as "terrorists", were shot dead.
Russia's defence ministry said the attackers were from a former Soviet republic, without elaborating. A senior Ukrainian official, Oleksiy Arestovych, said the two men were from the mainly Muslim Central Asian republic of Tajikistan and had opened fire on the others after an argument over religion.
Reuters was not immediately able to confirm the comments by Arestovych, a prominent commentator on the war, or independently verify casualty numbers and other details.
The shooting in Belgorod was the latest blow to Russian President Vladimir Putin's "special military operation" in Ukraine that started on Feb. 24.
Meanwhile, British military intelligence said Russia was facing more acute logistical problems in the south after the damage to the road-and-rail bridge linking mainland Russia to Crimea caused by the Oct. 8 blast.
A spokeswoman for Ukraine's Southern Military Command said Russian forces were suffering severe shortages of equipment because of the damage to the bridge.
Almost 75% of Russian military supplies in southern Ukraine comes across the bridge, Natalia Humeniuk told Ukrainian television, adding strong winds had also stopped ferries in the area.
"Now even the sea is on our side," Humeniuk said.
Russian officials said the explosion was caused by a truck bomb. Putin has branded the blast a "terrorist attack" orchestrated by Ukrainian security services.
Ukraine did not claim responsibility for the blast but celebrated it.