Ukraine announced that its forces have retaken three villages in the eastern region of Donetsk, the first reported gains of their new offensive.
But three people were killed and at least another 23 wounded as Russia shelled a rescue boat evacuating civilians from Russian-controlled territory, the Kherson region prosecutors' office said on Sunday.
Analysts at Washington-based think tank the Institute for the Study of War say that Kyiv's forces have launched counteroffensive operations in at least four front-line areas.
After months of building expectations, Ukrainian President Volodymyr Zelensky confirmed on Saturday that a counteroffensive against Russian forces had begun.
Then on Sunday, they announced the recapture of the three villages, the first significant gains in the new campaign.
"Neskuchne of the Donetsk region is under the Ukrainian flag again," said the state border guard service.
Earlier Sunday, Ukraine's army said its troops had taken the nearby village of Blagodatne. Ground forces released a video showing soldiers hoisting a Ukrainian flag over a destroyed building.
Military spokesman Valeriy Shershen said in televised remarks the village sat on the border of the eastern region of Donetsk and the southern region of Zaporizhzhia, where Moscow has reported heavy Ukrainian assaults over the past week.
Ukraine's forces had captured several Russian and pro-Russian troops, Shershen added.
Later Sunday, deputy defence minister Ganna Malyar said Ukraine's forces had retaken a third village, Makarivka, northwest of Blagodatne.
Major Ukrainian military successes in the Zaporizhzhia region could potentially enable its forces to break through the land bridge that connects Russia with the Crimean peninsula it annexed from Ukraine. This would be a major reversal for Moscow.
Russia's defence ministry said Ukraine had made an unsuccessful attack Saturday night on a Russian warship in the Black Sea. The Priazovye is on patrol duties monitoring the natural gas pipelines there.
The ministry said the attack, by drone boats, had been repelled and its vessel was not damaged.
Worst disaster 'since Chernobyl'
The civilians killed and wounded in the shelling of the rescue boat were caught in the fallout from Tuesday's destruction of the Russian-controlled Kakhovka dam along the front line in the southern Kherson region.
Ukrainian officials say seven people died and 35 people, including seven children, are still missing following the devastating flood unleashed by the dam's destruction.
While Ukraine accuses Russia of blowing up the dam on the Dnipro River, Moscow says Kyiv fired on it.
"This is the worst environmental catastrophe since Chernobyl so we are investigating not only a war crime but also an ecocide," Ukrainian Prosecutor General Andriy Kostin said after visiting the site with representatives of the International Criminal Court.
A total of 450 tonnes of turbine oil have spilled into the waters of the Dnipro and the Black Sea, he added.
Ukrainian Interior Minister Igor Klymenko said 77 towns and villages had been flooded in Kherson, where five people died, and Mykolaiv, where two died, while 162,000 people were without water supplies.
Zelensky said 4,000 people had been evacuated in the two regions.
Dropping water levels
An employee at Kherson's meteorological agency, Lora Musiyan, said the level of water had dropped by 1.7 meters (5.5 feet) from its peak measurements recorded last week.
In Kherson city, the largest population centre near the dam, the water has begun to subside enough to allow locals to return to assess the damage, an AFP correspondent at the scene said.
"The losses are significant. I don't even know what to do now," said Oleksiy Gesin, surveying the scene after his grocery store was flooded to chest height.
Damage to the dam may also be a problem for an upstream reservoir used to cool nearby reactors at Europe's largest nuclear power plant.
The International Atomic Energy Agency (IAEA) said its experts need access to a location near the Russian-occupied Zaporizhzhia nuclear power plant to assess "a significant discrepancy" in water level measurements, as well as to the electrical switchyard at the thermal power plant.
"Even though the (plant) has not been producing electricity for several months now, it still needs access to water and power for cooling and other essential safety and security functions and to avoid the risk of a potential fuel meltdown and release of radioactive material," the IAEA said in a statement.