According to the country's deputy defence minister, "extremely fierce battles" are going on in several areas of Ukraine as Kyiv's forces continue their counteroffensive.
Ukrainian soldiers have advanced close to Bakhmut in the east and Zaporizhzhia in the south, according to a Telegram post by Hanna Maliar.
She did, however, admit that in certain places, Russian soldiers were putting up a strong defence.
Her remarks follow yet another night of Russian missile and drone attacks on Ukrainian cities.
Despite Russian President Vladimir Putin's admission that his army lacks drones and missiles, Russia has intensified its bombing campaign recently.
According to the Ukrainian army, industrial facilities in the Dnipropetrovsk area were the target of nocturnal strikes on Thursday morning. A series of drone strikes on the Black Sea city of Odesa were thwarted, according to regional military spokesman Serhiy Bratchuk.
Three individuals had been slain the day before in an attack on an Odesa warehouse and a retail mall.
It has taken a long time for Kyiv to make its much-anticipated push, and Ukrainian authorities accuse Russia of stepping up its attacks in recent weeks to draw attention away from the onslaught.
Since beginning their counteroffensive, the Ukrainians claim their soldiers have retaken seven villages and at least 90 sq km (35 sq miles).
According to Ms. Maliar's Telegram post, Ukrainian troops have advanced near Bakhmut, which has long been the scene of a deadly and gruelling street-by-street conflict with Russian forces.
According to her, soldiers moved 300 to 500 metres in the southern Zaporizhzhia region and 200 to 500 metres in the direction of the city. The BBC is unable to independently confirm these assertions.
She did, however, acknowledge that some "extremely fierce battles" had already been sparked by the counteroffensive, as Ukrainian forces attempted to breach established Russian defensive lines.
Senior Western officials have cautioned against assuming that Russian soldiers will simply "melt away" in the face of Ukrainian advances, noting that Kyiv's gains have already been "costly".
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