Although tougher battles lie ahead, and the land recaptured in just over a week is a fraction of the territory Russia holds in Ukraine, the advances are Kyiv's biggest in several months.
"We are ready to continue fighting to liberate our territory even with our bare hands," Brigadier-General Oleksii Hromov told a media briefing.
He confirmed Russian troops that invaded in February 2022 had been forced out of seven settlements in the eastern region of Donetsk and in the southern region of Zaporizhzhia.
The army has advanced by up to 3 km (1.8 miles) near the village of Mala Tokmachka in the Zaporizhzhia sector and by up to 7 km near a village south of Velyka Novosilka in the Donetsk sector, he said.
The military said its forces had also advanced in the Donetsk region around the Russian-held city of Bakhmut and near the city of Vuhledar, but made clear fighting was intense.
"Our units and troops are moving forwards in the face of fierce fighting, (and) aviation and artillery superiority of the enemy," Valeryi Shershen, a spokesperson for the Tavria military sector of southern Ukraine, told Ukrainian television.
Reuters could not verify the battlefield situation. Russia has not officially acknowledged the Ukrainian advances, and says Ukrainian troops have suffered heavy casualties, but Reuters has confirmed the liberation of at least two villages.
Russia launched heavy air strikes as the counteroffensive was being prepared, and has carried out more air attacks since it began.
"The only thing that changes is the priority of the targets, the time of the strike and the intensity, accordingly," air force spokesperson Yuriy Ihnat told a separate briefing.
He said air strikes on the capital Kyiv in May were intended partly to cause panic and portray Russian weapons as superior to those provided by Ukraine's NATO allies.
(Reporting by Pavel Polityuk, Writing by Anna Pruchnicka, Editing by Timothy Heritage)
