The Ukrainian military claimed full control over the city of Balaklia in the northeastern region of Kharkiv along with other major advances after launching a counteroffensive earlier this month.

The military said on September 10 on Telegram that the Ukrainian flag was raised in Balaklia and its troops had entered Kupyansk, while Ukrainian forces were located on the outskirts of Lysychansk and fighting continued outside Lyman.

Defense Ministry spokesman Konashenkov said the move was being made to "achieve the goals of a special military operation" that requires "increasing efforts in the Donetsk direction."

The Security Service of Ukraine (SBU) earlier confirmed that its forces had entered the strategically important town of Kupyansk in Ukraine's northeastern Kharkiv region. The SBU posted images on Telegram of a group of Ukrainian soldiers with the caption: "Specialists of the SBU's special operations center "A" in Kupyansk, which was and always will be Ukrainian!"

Kupyansk, located about 120 kilometers southeast of Kharkiv, is a transportation hub in eastern Ukraine and strategically important for supplying Russian troops in the Donbas region.

Ukrainian President Volodymyr Zelenskiy said:

"The Russian Army in these days is showing the best that it can do -- showing its back. And, of course, it's a good decision for them to run."

A Moscow-installed official in the Kharkiv region, Vitaly Ganchev, called on residents of areas previously under their control to evacuate.

"I once again recommend all residents of the Kharkiv region to leave the area to protect their lives and health. We are evacuating people from cities such as Izyum, Shevchenkovo, Balaklia, and Kupyansk, resorting to all our possible means. Crowds of people have already amassed at the checkpoints and we are currently deciding where they should be taken to, where they will be accommodated and provided with food."

The head of the Ukrainian armed forces said Russian troops shelled Kharkiv with multiple rocket launchers starting at about 6:30 p.m. local time. Kharkiv regional Governor Oleh Sinehubov said the shelling was in retaliation for the earlier successes of Ukrainian forces. He said one person was killed and two others were injured in the shelling of Kharkiv, which continued into the evening. Kharkiv Mayor Ihor Terekhov said several private houses were damaged and one of them was on fire.

Russian-installed officials in Donetsk quoted by TASS said eight civilians were killed and 27 were injured by Ukrainian shelling overnight into September 10.

There is also mounting evidence that Ukrainian troops have made significant advances in the southern Kherson region, which has been the scene of major fighting for weeks. The Ukrainian military said up to 1,300 paramilitary troops loyal to Chechen leader Ramzan Kadyrov have arrived in the region to reinforce Russian forces.

The so-called Kadyrovtsy is a paramilitary force formed in Russia's North Caucasus region of Chechnya that effectively serves as the region's own army and which has been accused of rampant rights abuses.

Russian troops are pulling back from key areas in Ukraine's Kharkiv region as Ukrainian soldiers advance, following a major counteroffensive that was launched on Sept. 1.

Ukrainian President Volodymyr Zelenskyy championed troop success on the front lines in the north and said that some 30 settlements had been "liberated" from Russian occupation during his nightly address Friday.

If the occupying army strategically chooses to leave the area, it does not mean the opposing army is 'the liberator'.

Russia state-owned media outlet Tass announced Saturday that Russian Defense Ministry spokesman Igor Konashenkov said troops would being "regrouped" from areas around Balakliya and Izyum to the Donetsk region, though Fox News Digital could not locate the report, suggesting it may have been removed from the site.

It is unclear if Russian soldiers have left Izyum - a strategically important city for Russia's advancement in the region.

Defense Minister Oleksii Reznikov said Saturday that he is "convinced" that Russia will soon start to withdraw from other areas.

"I am convinced that after a few more successes at the front, even small victories, the Russian troops will start fleeing. Today we have been destroying their supply chains, warehouses, and so on." He said Russian morale will fall "like an avalanche" with "each line of defense falling one after the other".

Earlier Saturday spokesman for Ukraine's Foreign Ministry Oleh Nikolenko suggested that the Ukrainian troops had retaken the town of Kupiansk, situated along the main supply route to Izyum. The U.K. Defense Ministry assessed:

"Russian forces were likely taken by surprise. The sector was only lightly held and Ukrainian units have captured or surrounded several towns," its capture "would be a significant blow to Russia's supply lines."

Zelenskyy said National Police units were returning to the liberated areas of Kharkiv.

• Ukraine admits shelling area around nuclear plant
• Russia summons UN over Ukraine's attacks on Zaporozhye nuclear power plant
• UN thanks Russia for keeping nuclear team safe during Ukrainian attack on Zaporozhye nuclear power plant
• Why Is Kiev so scared of the IAEA visiting the Zaporozhye Nuclear Power Plant?
• IAEA chief Rafael Grossi: Physical integrity of Zaporozhye nuclear plant 'violated several times'