Ukrainian President Volodymyr Zelensky said Russia needed to "feel" the consequences of its war as a major Ukrainian incursion across the Russian border stretched into a third day.

According to the Russian army, Pro-Kyiv forces stormed into Russia's southwestern Kursk region on deploying around 1,000 troops and more than two dozen armoured vehicles and tanks.

Reports have it that Ukrainian incursion appears to be the most significant Ukrainian attack into Russia since the war began, with independent analysts suggesting Kyiv's troops had advanced up to 10 kilometres into Russia.

Zelensky said in his address, without directly referring to the offensive that Ukrainians know how to achieve their goals.

Similarly, Russia's Defence Ministry said its troops were continuing to destroy armed Ukrainian units and were using air strikes, rocket and artillery fire to push them back.

Meanwhile, the independent US-based Institute for the Study of War said Ukraine had made significant territorial gains in the first two days of the incursion.

It revealed that Ukrainian forces made confirmed advances up to 10 kilometres into Russia's Kursk Oblast amid continued mechanised offensive operations on Russian territory.

The institute stressed that the current confirmed extent and location of Ukrainian advances in Kursk Oblast indicating that Ukrainian forces have penetrated at least two Russian defensive lines and a stronghold.