KYIV, Ukraine (AFP) — Seven civilians have been killed and three injured in the Ukraine city of Bakhmut in the eastern Donetsk region, the regional governor said Tuesday.

Three bodies of civilians killed earlier were also discovered in two places in the region, which has been at the center of intense fighting with the Russian army for months, Governor Pavlo Kyrylenko said on Telegram.

The Ukrainian army said Russian troops were on the offensive in the Donetsk region towards the cities of Bakhmut and Avdiivka.

On Monday, Ukrainian troops said they had pushed back Russian assaults around 10 settlements in the eastern regions of Donestk and Lugansk, including near the city of Bakhmut.

In September the Ukrainian army claimed thousands of square kilometers in counteroffensives in the northeast and the south.

Battles now center on the east and in the south towards Kherson.

Donetsk is one of the four Ukrainian regions that Russian President Vladimir Putin claims to have annexed, and where martial law has been imposed.

Meanwhile, five people were injured in a blast Tuesday in the Russian-held city of Melitopol in southern Ukraine, the pro-Moscow administration said.

"A car exploded near the ZaMedia media group building in Melitopol," damaging it and nearby residential homes, the local pro-Moscow administration said on Telegram, adding that "five people were slightly injured, including employees of the media group. One was hospitalized."