In Vilhivka, a village east of Kharkiv held by Ukrainian forces, the thump of artillery and swoosh of rocket launchers is heard from fighting at the front.

That fighting has now pushed further east, where Ukraine has been trying to capture the banks of the Donets river and threaten Russian supply lines on the far side.

Following days of advances, Ukrainian forces were within several kilometres of the Russian border in the Kharkiv region on Wednesday morning, one Ukrainian military source told Reuters.

East of Vilhivka, Ukrainian forces seemed to be in control of the village of Rubizhne, on the banks of the Donets, after what appear to the be the fastest advances since April when Ukraine pushed Russian forces back from Kyiv and the country's north.

"It is burned out, just like all Russian tanks," a Ukrainian soldier told Reuters outside the village next to the ruins of one Russian tank. "The weapons are helping a lot, the anti-tank ones."

President Volodymyr Zelenskiy's office said Russian forces were "gradually being pushed out of Kharkiv", though Kyiv has so far confirmed few details of the advance through the region, preferring to remain cautious.

Zelenskiy himself said the successes were putting the second largest city - under constant bombardment since the war's early days - beyond the range of Russian artillery, but he cautioned Ukrainians against raising expectations too high yet.

"We should not create an atmosphere of excessive moral pressure, where victories are expected weekly and even daily," he said in an overnight video address.

The 92nd Mechanised Brigade confirmed to Reuters on Tuesday that it had recaptured four villages north of Kharkiv, pushing Russian forces closer to the border.

"The enemy is trying to prevent our troops from moving further towards the border in the Kharkiv region," the Ukrainian general staff said, without providing specifics.

Ukrainian progress could be seen on the ground in Vilhivka, a severely damaged village recaptured by Ukrainian forces weeks ago but where few civilians had so far dared return.

With the Russians having now been pushed further east in recent days, more people were now venturing back to comb through the wreckage of their homes.

Wednesday's separate move by Ukraine to cut off Russian gas supplies through territory held by Russian-backed separatists was one of the first times gas shipments to Europe have been directly affected by the conflict.

Gas flows from Russia's export monopoly Gazprom to Europe via Ukraine fell by a quarter after Kyiv said it was forced to halt all flows from the Sokhranovka transit point in southern Russia, because Russian-backed separatists were siphoning supplies.

Should the supply cut-back persist, it would be the most direct impact so far on European energy markets of the war that the Kremlin calls a "special military operation".

Apart from the east, Russia has seized a swathe of southern Ukraine, where Kyiv and its Western allies say they believe Moscow intends to organise a fake referendum on independence or annexation to make its occupation permanent.

The Kremlin said on Wednesday it was up to residents living in the Russian-occupied Kherson region to decide whether they wanted to join Russia, but any such decision must have a clear legal basis.

Earlier, TASS news agency quoted an official in the Russian-controlled administration as saying the region planned to ask President Vladimir Putin to incorporate it into Russia.

Russian forces have also continued to bombard the Azovstal steelworks in the southern port of Mariupol.

Ukraine's general staff said Moscow was trying to capture the last bastion of Ukrainian resistance in the ruined city.

The Azov Regiment holed up inside it said Russia was bombing the factory from the air and trying to storm it. Reuters was unable to independently verify the reports of fighting there.

Australian Associated Press