After their initial failed advance on the capital Kyiv in the first weeks after the February 2022 invasion, Russian troops have focused on capturing all of Donetsk region in eastern Ukraine.
The city of Kostiantynivka has been a major target.
Ukrainian forces have for months defended the city against fierce assaults, with the regional governor urging remaining residents this week to leave as infrastructure breaks down.
Top Ukrainian commander Oleksander Syrskyi, writing on Telegram on Saturday, said the area around Kostiantynivka was gripped by heavy fighting.
"The enemy is surging towards Kostiantynivka but apart from sustaining numerous losses, has achieved nothing," Syrskyi said.
"The aggressor is trying to break through our defences and advance along three operating sectors."
A spokesman for Ukrainian forces in the east, Viktor Trehubov, told the Ukrinform news agency that Kostiantynivka and the city of Pokrovsk to the west were "the main arena of battles and the Kremlin's strategic ambitions".
Syrskyi also said that Ukrainian forces had withstood in the past week a powerful attack near the village of Yablunivka in northeastern Sumy region, where Russian forces have been trying to establish a buffer zone inside the Ukrainian border.
Russia's Defence Ministry, in a report earlier in the day, said its forces had seized the village of Chervona Zirka - further southwest, near the administrative border of Dnipropetrovsk region.
Russia's slow advance through eastern Ukraine, claiming a string of villages day after day, has resulted in destruction of major cities and infrastructure.
Russian authorities have insisted that progress towards a settlement of the 40-month-old war depends on Ukraine recognising Russia's control over four Ukrainian regions - Luhansk, Donetsk, Zaporizhzhia and Kherson.
Russian forces control about one-fifth of Ukraine's territory although they do not fully hold any of the four regions.
Russia has said in recent weeks that its troops have made advances in areas adjacent to Dnipropetrovsk region, which lies next to both Donetsk and Zaporizhzhia regions.
Ukrainian officials have denied those reports.
