Russian forces have entered Sudzja from several directions, according to, among others, the think tank Institute for the Study of War (ISW). According to Russian military bloggers, cited by Western media, Russian soldiers have raised flags in the city's square to mark its recapture.
Sudzja is located half a mile northeast of the border with Ukraine, along a highway that has been an important supply route for Ukrainian forces since they broke into Russian Kursk in an unexpected offensive last summer.
On Wednesday, Russia's Defense Ministry also claimed to have captured several locations around Sudzja.
The town is devastated and abandoned, but has still been seen as an important foothold for the Ukrainians. This is especially true now, as talks about a ceasefire are ongoing and both parties are eager to have as strong a bargaining chip as possible.
There has been speculation that Ukraine could exchange captured territory in Kursk for areas that Russia has seized in its invasion of eastern Ukraine.
And the Ukrainian army is apparently still on the attack. On Wednesday, Russian authorities reported that four civilians were killed when a factory in Kozyrevka, further into Russia than Sudzja, was hit.
"Four employees were killed, three men and one woman," wrote a regional official according to the AFP news agency.