Video released by the unit shows a small group carrying a blue and yellow stake to the border line.
The Ukrainian military said on Monday that around Kharkiv “the enemy is concentrating its main efforts on maintaining its positions and preventing the advance of our troops” in the direction of the border.
Over the past few days, Ukrainian forces advanced toward the border in several places north and east of Kharkiv, the country’s second largest city before the invasion began, as Russian forces have withdrawn.
Ukrainian officials said last week they were liberating villages on the outskirts of the city.
Their advances threaten the symbolic embarrassment of expelling the Kremlin’s forces back to their own border while posing the strategic threat of cutting Russia’s supply lines into Ukraine and its forces further south in the Donbas region.
Ukrainian troops on Monday resisted attempted Russian advances and even rolled back the front lines in places. Over the past few days, Moscow’s forces pulled back from around the northeastern city of Kharkiv after bombarding it for weeks.
And a glimmer of hope emerged for wounded Ukrainian troops trapped in the bombed remains of a giant steel plant, the last stronghold of resistance in the port city of Mariupol.
The Russian Defence Ministry announced an agreement for the wounded to leave the steelworks for treatment in a town held by pro-Moscow separatists.
There was no immediate confirmation from the Ukrainian side, and there was no word on whether the wounded would be considered prisoners of war. Nor was it clear how many fighters might be evacuated.
As fighting raged in eastern Ukraine, the international response to Russia’s attack continued to pick up pace.
Russian President Vladimir Putin, who launched the invasion in what he said was an effort to check NATO’s expansion but is now seeing that strategy backfire, warned that a military buildup on the two countries’ territory “will of course give rise to our reaction in response”.
NATO Secretary-General Jens Stoltenberg has said the membership process for both Finland and Sweden could be very quick, though member Turkey has expressed some reservations about the move.
Swedish Prime Minister Magdalena Andersson said that joining the 30-member military alliance is her country’s best defense in the face of Russian behaviour.
“Unfortunately, we have no reason to believe that the trend (of Russia’s actions) will reverse in the foreseeable future,” she said.
Europe is also working to choke off funding for the Kremlin’s war by reducing the billions of dollars it spends on imports of Russian energy.
But a proposed EU embargo on imports of Russian oil faces opposition from a small group of countries led by Hungary, which is one of a number of landlocked countries highly dependent on the imports, along with the Czech Republic and Slovakia. Bulgaria also has reservations.