The Armed Forces of Ukraine said that the Russians have sent about 500 troops from occupied areas of the Donetsk and Luhansk regions north into the Kharkiv region.
They gave no explanation for the move, but CNN reported earlier Tuesday comments by local officials in the Kharkiv region that suggested some Russian troops were being sent northward to reinforce supply lines from the border.
Local authorities said there is "a mass withdrawal of Russian troops from the territory of Borova and Bohuslavka in the direction of Kupyansk."
Kupyansk is an important Russian logistics hub inside Ukraine and may become vulnerable if a Ukrainian counterattack in the region is sustained.
That attack made further progress Tuesday, according to the General Staff of the Ukrainian Armed Forces, with four more settlements to the north and east of Kharkiv falling under Ukrainian control.
CNN has geolocated video from one of those settlements, showing the Ukrainians in control. The new gains put Ukrainian units within a few kilometers of the Russian border in several areas.
Elsewhere in Ukraine, the Ukrainians said Russian forces continue to try to take the town of Rubizhne in Luhansk region, but without success. Officials said Ukrainian units had withstood several attacks in the Luhansk region.
In the Donetsk region, the General Staff said the Russians were trying to break through Ukrainian defenses north of Sloviansk, around the settlements of Oleksandrivka and Shandryholove.
This area has seen almost constant fighting for around two weeks, but the Russians appear to have made minimal progress on the ground.
Overall, the General Staff's report suggests that Ukrainian units are under pressure but resisting on most fronts while taking territory in Kharkiv as the Russians fall back toward the Oskil river.