"If we talk about the entire frontline, both east and south, we have seized the strategic initiative and are advancing in all directions," Deputy Defense Minister Hanna Maliar told Ukrainian television.
Maliar said Ukrainian troops were moving "confidently" on the flanks around the devastated eastern city of Bakhmut, which is held by Russian forces, and the main fighting was going on around the city.
In the south, Kyiv's forces were moving with mixed success and mainly levelling the frontline, she said.
"In the south, we are moving with varying success, sometimes there are days when it is more than a kilometer, sometimes less than a kilometer, sometimes up to 2 kilometers" she said.
"Therefore, all these tasks are being carried out and only the military can assess this correctly and accurately, and according to their assessment, everything is going according to plan," Maliar said.
Since the start of the counteroffensive this month, Ukraine says it has reasserted control over clusters of villages in the southeast although Russia still holds swathes of territory in the east, south and southeast.
Reuters was unable to verify the situation on the battlefield. Russia, which began its full-scale invasion in February 2022, has not acknowledged the Ukrainian gains and has said Ukraine's military are suffering heavy casualties.
President Voldoymyr Zelenskiy has described the counteroffensive as proceeding more slowly than desired, but that Kyiv would not be pressured into speeding it up.
Ukrainian officials have also said the "main event" of the counteroffensive has yet to start, and that Ukraine has not yet sent its main troop reserves into combat.