Ukrainian troops are “strengthening” positions in territories captured by Russia and are expanding further, President Volodymyr Zelensky said.
Ukrainian soldiers have been pushing into Russia’s Kursk region for two weeks, their deepest since Moscow launched its full-scale invasion more than two years ago.
Troops continue to advance towards Kursk, the force said in its daily report.
Moscow called the raid a serious provocation and vowed to respond with a “worthy response.”
In a statement on the Telegram messaging app, President Zelensky said: “Thank you to all the soldiers and commanders who are taking Russian military prisoners and bringing closer the release of our soldiers and civilians detained by Russia.
“General Syrskyi also reported on the strengthening of the positions of our forces in the Kursk region and the expansion of the stabilized territory.”
Russia said its forces had pushed back Ukrainians near three settlements in the Kursk region and were hunting for “mobile enemy groups” trying to push deeper into the country.
Kiev claims to have taken control of more than 80 settlements during the incursion.
His latest statement comes after Ukraine strategically important bridge destroyed on the Seym River this week.
The bridge had been used by the Kremlin to supply its troops and its destruction could have hindered those efforts.
The Russian Foreign Ministry said the bridge was “completely destroyed” and that volunteers assisting the evacuated civilian population were killed.
However, as Ukraine advances further into western Russian territory, Russian forces are also gaining ground in eastern Ukraine and have reclaimed a number of villages in recent weeks.
According to official Ukrainian sources, Russia attacked at least four Ukrainian regions on Saturday, including the northeastern Kharkiv region.
On Saturday, Mr Zelensky said there had been “dozens of Russian attacks” on Ukrainian positions near the towns of Toretsk and Pokrovsk.
Pokrovsk is a major logistics hub located along a major supply route to Ukrainian troops on the Eastern Front.
“Our soldiers and units are doing everything to destroy the occupier and repel the attacks,” the Ukrainian president said, stressing that the situation was “under control.”