President Volodymyr Zelensky has confirmed reports his military had retaken some villages but cautioned against expecting victory.
A spokesman for the Ukrainian military said settlements of Cherkaski Tyshky, Ruski Tyshki, Borshchova and Slobozhanske were back in Ukrainian hands as the campaign continues to stutter for Vladimir Putin’s forces.
Kharkiv and the surrounding area have been under sustained Russian attack since the early in the war.
Mr Zelensky that the military was gradually pushing Russian troops away from the city. The Ukrainian military’s general staff said its forces drove the Russians out of four villages to the northeast of Kharkiv as it tries to push them back toward the Russian border.
Russian forces have however made advances in the Donbas and control more of it than they did before the war began.
Fighting is also continuing for the strategic stronghold of Zmiinyi Island, also known as Snake Island.
According to an update from the Ministry of Defence (MoD) Russia is repeatedly trying to reinforce its exposed garrison on the island, but Ukraine successfully struck Russian air defences and resupply vessels with Bayraktar drones, with Russia’s resupply vessels now having minimal protection.
In an update, the MoD said: “Fighting continues at Zmiinyi Island, also known as Snake Island, with Russia repeatedly trying to reinforce its exposed garrison located there.
"Ukraine has successfully struck Russian air defences and resupply vessels with Bayraktar drones. Russia’s resupply vessels have minimum protection in the western Black Sea, following the Russian Navy’s retreat to Crimea after the loss of the Moskva.
"Russia’s current efforts to augment its forces on Zmiinyi Island offer Ukraine more opportunities to engage Russian troops and attrit materiel.”
It added: “If Russia consolidates its position on Zmiinyi Island with strategic air defence and coastal defence cruise missiles, they could dominate the north-western Black Sea.”
The island is of strategic importance because it provides access to Ukraine's major port cities, namely Odesa.
With Russian forces struggling to gain ground in the Donbas, military analysts suggest that hitting Odesa might serve to stoke concern about southwestern Ukraine, thus forcing Kyiv to put more forces there.