The fighting is raging in Ukraine's Lysychansk region, but the city is not encircled, the Ukrainian army said on Saturday.
Earlier Saturday the separatist group had said that they had encircled the city.
Andrei Marotchko, a spokesman for the separatist forces, earlier told the TASS news agency: "Today the Lugansk popular militia and Russian forces occupied the last strategic heights, which allows us to confirm that Lysychansk is completely encircled."
After the separatist spokesman made the allegations earlier in the day, Ruslan Muzytchuk, a spokesman for the Ukrainian National Guard, said on Ukrainian television that "Fighting rages around Lysychansk. (But) luckily the city has not been encircled and is under control of the Ukrainian army,"
Capturing the city would allow the Russians to push deeper into the wider eastern region of the Donbas, which has become the focus of their offensive since failing to capture Kyiv after launching their military operation in Ukraine in late February.
Across the Donets river from Lysychansk, the Russians seized the neighbouring city Severodonetsk last week.
