Kyiv said on Friday its incursion into Russian territory had advanced, claiming it aimed to force Russia to negotiate on "fair" terms, as Moscow's troops announced new gains in eastern Ukraine.

Kyiv's troops last week launched a major counter-offensive into Russia's Kursk region, sending more than 120,000 people fleeing.

The head of the Ukrainian military Oleksandr Syrsky told President Volodymyr Zelensky on Friday that "the troops continue to fight and have advanced in some areas from one to three kilometres (0.6 to 1.8 miles) towards the enemy."

The president said in his evening address: "We see that the occupier is suffering losses, and this is useful, very useful for our defence."

Zelensky's aide Mykhailo Podolyak said earlier Friday that Ukraine wanted to negotiate "on our own terms" by inflicting "significant tactical defeats on Russia".

"We have absolutely no plans to beg: 'Please, sit down to negotiate', he wrote on X, saying that Kyiv in the Kursk region is using military means to "persuade Russia to enter a fair negotiation process".

President Vladimir Putin has said Russia would declare a ceasefire only if Kyiv withdraws from the four regions that Russia claims to have annexed but only partially controls -- Donetsk, Lugansk, Zaporizhzhia and Kherson.

Ukraine meanwhile claims to have seized more than 1,100 square kilometres of Russian territory, in the biggest attack by a foreign army on Russian soil since World War II. (AFP)