Russia said on Friday it was dispatching reinforcements to the Kharkiv region in eastern Ukraine where Kyiv's forces have announced robust gains as part of a broader counter-offensive.

State media broadcast footage of columns of Russian tanks, support vehicles and artillery travelling along paved roads and dirt tracks, emblazoned with the letter "Z", the symbol of Moscow's invasion.

US Secretary of State Antony Blinken said that Russia's push to send reinforcements showed Moscow was paying "huge costs" in its bid to capture and hold Ukrainian territory.

A Moscow-installed official in the region, Vitaliy Ganchev, said in televised remarks that "fierce battles" were under way near Balakliya, a town in the Kharkiv region that Ukraine said it had recaptured on Thursday.

"We do not control Balakliya. Attempts are being made to dislodge the Ukrainian forces, but there are fierce battles and our troops are being held back on the approaches," Ganchev said.

"Now Russian reserves have been brought there, our troops are fighting back," he added.

His comments come after President Volodymyr Zelensky shared footage late on Thursday showing camouflage-clad Ukrainian soldiers holding his country's blue-and-yellow flag in Balakliya.

The town, which had been under Russian control for around six months and had a pre-war population of around 30,000 people, fell easily and early on to Russian forces who invaded in February.

The road from Kharkiv -- Ukraine's second-largest city -- heading southeast towards recaptured Balakliya was open Friday, AFP journalists said, with queues at several checkpoints and civilian and military vehicles dotting the road.

Zelensky said Thursday that in total Ukrainian forces had clawed back from Russian forces some 1,000 square kilometres (nearly 400 square miles) since the beginning of the month.

In the area around Kharkiv city, Ukrainian forces penetrated 50 kilometres (30 miles) beyond Russian lines and took back more than 20 towns and villages, military officials said earlier.

The counter-offensive has showed progress in the south of the country too, particularly in the Kherson region, as well as in Kharkiv and in the industrial Donbas province in the east.

There, a regional governor Pavlo Kyrylenko said that Russian attacks on the frontline city of Bakhmut killed eight people and wounded 17 others.

Bakhmut, with an estimated population of 70,000, "has been without water and electricity for the fourth day," he said, adding that "repairs are impossible due to ongoing fighting".

In one eastern Ukraine village, children have been adapting to their new reality by donning camouflage and manning pretend checkpoints.

It is a game many children have been playing throughout the summer on roads throughout the war-torn Donbas and Kharkiv regions.

"We stand here and stop cars to check if the people are Russian," said Nazar, 11, conjuring a menacing look.

"We stop them and say: 'the 93rd brigade salutes you'" he said, referring to a unit fighting in the northeast Kharkiv region near Russia.

Blinken's comments on the cost of the war came during a visit to Brussels on Friday where he was meeting with NATO Secretary General Jens Stoltenberg.

The Secretary of State said President Vladimir Putin's decision to send reinforcements towards Kharkiv region underlined the scale of Russia's military losses.

"There are a huge number of Russian forces that are in Ukraine and unfortunately, tragically, horrifically President Putin has demonstrated that he will throw a lot of people into this at huge cost to Russia," he said.

His assessment comes just one day after a surprise visit to Kyiv during which he unveiled another $2.8 billion in military aid for Kyiv and hailed Ukraine's "clear and real" frontline gains.

Defence Secretary Lloyd Austin said during a visit to Prague that Ukrainian troops were using US-supplied weapons and were "successfully changing the dynamics on the battlefield".

Key to the Ukrainian advances have been a steady stream of Western-donated weapons.

Long-range precision artillery has played a particularly crucial role, allowing Kyiv to disrupt Russian supply lines.

"So we see success in Kherson now, we see some success in Kharkiv, and so that's very, very encouraging," he added.