Plans for the counteroffensive come as Russia pushes forth its attempt to capture Bakhmut. Meanwhile, Medvedev has threatened that Russia might attack Kyiv or Lviv.
Ukrainian troops are reportedly preparing for a counterattack, after months on the defensive amid Russia's ongoing campaign to capture the eastern town of Bakhmut.
Oleksandr Syrskyi, Ukraine's top ground forces commander, was cited by the Reuters news agency as saying that Russia's private Wagner mercenaries were "losing considerable strength" and "running out of steam." The group has been at the forefront of Russia's eastern and southern assaults.
"Very soon, we will take advantage of this opportunity, as we did in the past near Kyiv, Kharkiv, Balakliya, and Kupiansk," he said, listing Ukrainian counter-offensives last year that recaptured swathes of land.
Ukraine's General Staff said in a report on Friday that Russian attacks on the towns of Lyman, Avdiivka, Mariinka, and Shakhtarske were all unsuccessful. Moscow's main focus however remained Bakhmut.
Russia has been struggling to capture the town for months, stressing the move would be strategic while Western analysts downplay its importance.
Capturing Bakhmut would not only give Russian fighters a rare battlefield gain after months of setbacks but could also rupture Ukraine's supply lines, allowing Moscow's forces to advance toward other Ukrainian strongholds in the eastern Donetsk region.