A THREE-year-old was among those wounded after a Russian missile strike hit the city of Lviv on Monday - which killed seven and injured 10 others.

Lviv Mayor Andriy Sadovyi posted a video on Twitter showing Artem — who he said traveled hundreds of miles to Lviv with his mother to flee Russian bombings in Kharkiv — receiving medical attention on his hand.

Doctors could be seen in the video operating on the youngster's left hand and then wrapping it with tape as a few people watched by his side.   

Iuliia Mendel, a former spokesperson of Ukrainian President Volodymyr Zelenskyy, said on Twitter that Artem lost part of his finger in the attack. 

On Monday morning, Ukrainian authorities said three Russian missiles struck military infrastructure in Lviv, and a fourth hit a tire fitting shop in the city.

Plumes of thick, black smoke were seen across Lviv after the explosions, with one Ukrainian adviser describing the attack as "barbaric".

After the humiliating sinking of the flagship of Russias Black Sea Fleet last week in what the Ukrainians boasted was a missile attack, the Kremlin had vowed to step up airstrikes.

Lviv has not seen a large amount of fighting during Russia's invasion, although there have been a handful of airstrikes.

The city has been used as hub by refugees fleeing to Poland - about 70km away from its border.

Russia's intense shelling across the country over the last few days marks the start of a new operation to achieve its goals - the "complete liberation" of the Donbas, broadly referring to Ukraine's eastern regions of Donetsk and Luhansk.

In a concerning assertion, Ukraine's President Volodymyr Zelenskyy said on Sunday night's address Russia wants to "finish off" Ukraine's Donbas region and wipe some places "off the face of the Earth". 

The Donbas - made up of Luhansk and Donetsk - has seen heavy fighting between Ukrainian forces and pro-Russian separatists since 2014.