STORY: Video posted on social media on Friday (August 9) and verified by Reuters showed a convoy of burnt-out Russian military trucks along a highway in the Kursk region of southern Russia.

It's the latest sign of the destruction after Ukrainian forces staged a major cross-border incursion this week.

Ukrainian forces burst across the border on Tuesday (August 6) in a shock counter-offensive, after months of gradual Russian advances in eastern Ukraine.

:: MIC IZVESTIA/IZ.RU

The operation, while limited in scope, has managed to bring the war to a number of Russian towns and cities.

In response to the incursion, Russia on Friday declared a state of emergency in the Kursk region, and the ministry of emergencies released this video of Russian civilians evacuating.

Russia's military Chief of Staff Valery Gerasimov reported to President Vladimir Putin on Wednesday (August 7) that Russian troops had halted the advance and would push the Ukrainians back to the border.

:: Russian Defense Ministry

The Defense Ministry released this video on Friday claiming to show its forces destroying Ukrainian armored vehicles in the Kursk region.

But official statements, accounts from military bloggers and videos posted on social media indicated Russia was still struggling to achieve that goal, nearly 48 hours later.

:: 'Nachtigall' unit of Ukraine's Unmanned Systems Forces

The Ukrainian military on Thursday (August 8) released this video purporting to show Russian soldiers surrendering at a border crossing.

Ukrainian officials have not commented directly on the operation, but asserted the right to defend themselves by striking Russia wherever it posed a threat.

Russian President Vladimir Putin called the operation a serious escalation.

Ukraine's primary ally, Washington, has pressured Kyiv not to launch long-range attacks on Russia directly.

But Pentagon spokesperson Sabrina Singh on Thursday said Ukraine's incursion into Kursk was "consistent with U.S. policy."

"They are taking actions to protect themselves, from attacks that are coming from a region that are within the U.S. policy of where they can operate."

Meanwhile in another front in the fight, Ukrainian officials said Russian artillery hit a supermarket in the Ukrainian town of Kostiantynivka in the frontline Donetsk region on Friday.

Ukrainian officials said that ten people were killed and 35 were injured.