Ukrainian forces have secured combat control of areas where Russian troops entered the northeastern Kharkiv region earlier this month, President Volodymyr Zelenskyy said.
Meanwhile, two people were killed Saturday in an aerial attack on the city of Kharkiv, which is the region's capital, according to local officials.
Kharkiv is about 20 kilometers (12 miles) from the Russian border. Moscow's troops have in recent weeks captured villages in the area as part of a broad push, and analysts say they may be trying to get within artillery range of the city. Ukrainian authorities have evacuated more than 11,000 people from the region since the start of the offensive on May 10.
Our soldiers have now managed to take combat control of the border area where the Russian occupiers entered, Zelenskyy said in his nightly video address on Friday evening.
Zelenskyy's comments appeared to be at odds with those made by Russian officials.
Viktor Vodolatskiy, a member of Russias lower house of parliament, said Russian forces now controlled more than half of the town of Vovchansk, 3 miles (5 kilometers) inside the border, Russian state news agency Tass reported Friday.
Vovchansk has been a flashpoint for fighting since Russia launched the offensive in the Kharkiv region. Vodolatskiy was also quoted as saying that once Vovchansk was secured, Russian forces would target the cities of Sloviansk, Kramatorsk and Pokrovsk in the neighboring Donetsk region.
Independent confirmation of the claims wasn't immediately possible.
Russia's Kharkiv push appears to be a coordinated new offensive that includes testing Ukrainian defenses in the Donetsk region further south where Russia's Defense Ministry said Saturday that its forces had taken over the village of Arkhanhelske while also launching incursions in the northern Sumy and Chernihiv regions.
Russian President Vladimir Putin has said the Kremlin's army is attempting to create a buffer zone in the Kharkiv region to prevent Ukrainian cross-border attacks.
The Russian push is shaping up to be Ukraine's biggest test since Moscow's full-scale invasion on Feb. 24, 2022, with outnumbered and outgunned Ukrainian forces being pressed at several points along the about 1,000-kilometer (620-mile) front line that snakes from north to south in eastern Ukraine.
In addition to the ground offensive operation along Ukraine's northeastern border, Russia is continuing to bombard the Kharkiv region with missiles, guided aerial bombs and drones.
Regional Gov. Oleh Syniehubov said that two people were killed and 24 others wounded when an aerial bomb hit a large construction supplies store in the city of Kharkiv on Saturday afternoon, causing a huge fire to break out. He said that more than 200 people could have been inside the store. A second bomb hit the city's central park, Kharkiv Mayor Ihor Terekhov said.
Ukraine's problems have been mounting in recent months as it tries to hold out against its much bigger foe, and the war appears to be at a critical juncture.