Moscow said Monday that its forces had pushed forward a few kilometers along Ukraine's frontline, while Kyiv said its troops had repelled Russian attacks in various areas.
Much of the fighting was concentrated around the eastern city of Bakhmut, with 16 nearby settlements having been bombarded, according to Ukrainian military.
It comes after the head of Russia's mercenary Wagner Group said Sunday it had taken the village of Krasna Hora, on the northern edge of Bakhmut.
U.S. think tank the Institute for the Study of War said geolocated footage showed Russian forces have captured at least part of the village. However, the claims have not yet been independently verified.
Meanwhile, Poland's president has said the decision over whether or not to supply Ukraine with fighter jets is "not easy." He gave no confirmation over the likely outcome of the discussions.
NATO's Secretary-General Jens Stoltenberg said the request for aircrafts would be discussed Tuesday, when ministers meet in Brussels for a two-day defense summit. In further comments, he said there was "no sign" that President Putin is preparing for peace.