Russia's defence ministry said on Sunday its forces had repelled efforts by Ukrainian troops to advance in the Donetsk, Kherson and Mykolaiv regions, inflicting what it described as significant losses against the enemy.
The battlefield reports could not immediately be verified.
Russia also said it was continuing air strikes on military and energy targets in Ukraine, using long-range precision-guided weapons.
"The goals of the attacks have been reached. All the assigned targets have been neutralised," the ministry said.
Throughout the near eight-month conflict, Russian missiles have also struck civilian population centres in Ukraine. Russia denies targeting civilians in what it calls its "special military operation" in Ukraine which it launched on Feb. 24.
Russia said its forces had held positions during "fierce fighting" in the Kherson region and also inflicted blows on Ukrainian positions in the Donetsk region.
In Ukraine's Kharkiv region, Russia said it destroyed three U.S.-manufactured howitzers and a crossing point on the Oskil River, set up by Ukrainian forces to move reserves and ammunition.
The river flows south into the Siversky Donets, which snakes through the Donbas.
(Reporting by Reuters, Editing by Louise Heavens and Nick Macfie)