The Russian Defense Ministry said on Sunday that Russian forces reached Ukraine's Dnipropetrovsk region and continued their advance there.
It also said that Russian troops captured the village of Zoria in Ukraine's Donetsk region.
Moscow, which has the initiative on the battlefield, has repeatedly refused calls by Ukraine, Europe and US President Donald Trump for a full and unconditional ceasefire.
At talks in Istanbul last week it demanded Kyiv pull troops back from the frontline, agree to end all Western arms support and give up on its ambitions to join the NATO military alliance.
Dnipropetrovsk is not among the five Ukrainian regions over which Russia has asserted a formal territorial claim.
It is an important mining and industrial hub for Ukraine and deeper Russian advances into the region could have a serious knock-on effect for Kyiv's struggling military and economy.
Dnipropetrovosk was estimated to have a population of around three million people before Russia launched its offensive. Around one million people lived in the regional capital, Dnipro.