STORY: Explosions rang out and fires raged on Tuesday as Russian forces pressed forward with their weeks-long drive to encircle and capture the eastern Ukrainian city of Bakhmut -- a prize coveted by Russia.

But Ukrainian forces insisted they would not withdraw.

UKRAINIAN ARMY MEDIC: "We won't give up Bakhmut. We will hold on to it until the very last. Glory to Ukraine, death to the enemies."

Around the city, Russian troops and Wagner mercenary fighters are trying to cut the Ukrainian defenders' supply lines and force them to surrender or withdraw.

Capturing Bakhmut would be Russia's first major prize in more than six months and open the way for taking the last remaining urban centers in the Donetsk region, one of four Moscow claims to have annexed.

Russian President Vladimir Putin on Tuesday instructed his forces to bolster security in the four regions - currently only partially controlled by Russia.

Ukraine's military said Russia was shelling settlements around Bakhmut, which had a pre-war population of about 70,000 but now lies in ruins after months of intense trench warfare.

Despite the violent firefights echoing in the streets, some citizens remain.

LOCAL RESIDENT: “As long as my home is intact, as long as I am not hurt, I will stay here.”

While the city of Bakhmut hangs in the balance, a senior pentagon official said Tuesday the U.S. does not expect Russia to make significant territorial gains in the near-term, describing the front lines in the year-long war as a "grinding slog."