Russia has conceded for the first time that some Ukrainian forces have crossed onto the  Dnipro River's eastern bank, but has said they face "hell fire" and that the average life expectancy of a Ukrainian soldier there is around two days.

Ukrainian President Volodymyr Zelenskyy's chief of staff said Tuesday that Ukrainian forces had secured a foothold on the east bank of the Dnipro River in southern Ukraine's Kherson region, the first official acknowledgment of its kind.

Andriy Yermak said Ukrainian forces had managed to cross the river and dig in "against all odds" and his country's counteroffensive aimed at clawing back territory from Russia – which has so far failed to make a major breakthrough – was "developing."

Vladimir Saldo, the Russian-installed governor of the part of Kherson region which Moscow controls, acknowledged in a statement that Ukrainian forces had managed to cross the river which was seen by Russia as a difficult barrier for Kyiv's soldiers to surmount.

But citing what he said was first-hand information from Russia's 'Dnepr' military grouping, he said Russian forces had pinned the Ukrainians down and were raining "Hell fire" on them and predicted they would be wiped out.

Reuters could not independently verify his assertions.

"Our additional forces have now been brought in. The enemy is trapped in (the settlement of) Krynki and a fiery hell has been arranged for him: bombs, rockets, heavy flamethrower systems, artillery shells, and drones," said Saldo.

"They (the Ukrainians) are sitting in basements and run from one basement to another at night. In the last two or three days alone, total enemy losses have totaled about a hundred fighters."