KYIV: Eight people were killed and 13 injured on Saturday in Lyman in eastern Ukraine after the town came under Russian rocket fire, Ukraine's interior ministry said.

"So far we know about 8 dead... The number of injured has increased to 13 people," the ministry said on social media.

A residential building, an annexe to a printing house and three cars were set on fire in the attack, it said.

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Pavlo Kyrylenko, governor of the Donetsk region where Lyman is located, said "at around 10:00 am, the Russians struck the town with multiple rocket launchers".

Lyman, a major rail hub, was initially captured by Russian forces but then re-taken by Ukraine's army in October.

Ukraine has reported Russian offensive operations in the area this week.

In the Russian-controlled town of Oleshky in southern Ukraine, an emergency services official was quoted by TASS news agency as saying two civilians were killed by Ukrainian fire overnight.

Ukrainian forces last month began a counteroffensive to take back Russian-controlled territory in the east and south of the country.

Facing powerful Russian defensive lines, they have only recaptured a few hundred square kilometres and around a dozen villages after more than a month.