Russia was intensely attacking the eastern town of Avdiivka and southern village of Robotyne, where fighting has centred in recent weeks, Ukraine said on Monday.
Neither side has made significant breakthroughs on the battlefield for weeks, as Moscow's invasion drags on for a 22nd month.
In recent weeks, Russia has focused its efforts on the industrial hub of Avdiivka in the Donetsk region, which now appears almost encircled by Moscow's forces.
"The enemy continues offensive actions near Avdiivka," the Ukrainian army said.
It said Moscow's forces had launched "more than 150" attacks on Ukrainian positions in villages around the town.
A day earlier, Ukraine said it had "repelled" two dozen attacks around Avdiivka.
Kyiv did not report gains or losses in the area.
But the US-based Institute for the Study of War said "Russian forces made confirmed advances northwest and southeast of Avdiivka" over the weekend.
Moscow controls territory to the north, east and south of Avdiivka, which lies just 10 kilometres (six miles) from the Moscow-held city of Donetsk.
In the south, Kyiv said Russian forces had "conducted around 20 attempts to restore lost position near Robotyne of the Zaporizhzhia region, but gained no success."
Ukraine recaptured the tiny village of Robotyne in August, announcing a strategic victory in its counter-offensive.
But Russia has attacked Robotyne since, with Ukraine appearing to struggle to hold on.
Russian military bloggers, meanwhile, reported that Ukraine's positions established on the Moscow-held side of the Dnipro river were steady, despite Russian attempts to oust them.
Ukrainian forces reportedly crossed to the occupied bank of the river in the Kherson region earlier this month, establishing positions in the hamlet of Krynky, in a tactical success.
"The Russian army with the help of the artillery counter-attacked in Krynky and got back part of their positions," the WarGonzo Telegram account, close to the Russian army, said.
"But the foothold of the Ukrainian army in this village remains quite stable," the account added.