Near Bakhmut, Ukraine — Russia's Minister of Defense gave some indication Tuesday as to why his country has been willing to throw so many soldiers at the grueling battle to capture the small industrial city of Bakhmut in eastern Ukraine. Sergei Shoigu said capturing the town would enable Russian forces to push further into Ukraine, taking more ground in the Donbas region that Russian President Vladimir Putin has appeared desperate to seize in its entirety.

The Ukrainian forces battling street-to-street to hold onto the city are surrounded on three sides, but they have refused to back down. Some of the troops who've held that front line have told CBS News they can't understand why Russia has been willing to sacrifice so many lives, but it has not weakened their resolve.

• Civilians grapple with harrowing decisions as Russia's war closes in

Shoigu said Tuesday that taking Bakhmut was essential to Russia's "further offensive" in the Donbas. That acknowledgement may bolster Ukraine's commitment to prevent that from happening.

Ukrainian President Volodymyr Zelenskyy said Monday night that his military commanders had informed him they were not ready to give up, and he and other senior leaders "unanimously supported this position."

"I told the commander in chief to find the appropriate forces to help our guys in Bakhmut," Zelenskyy said.

And those guys will welcome any help they can get.

Ukrainian forces brought our team to a vital lookout point only about a mile and a half from the decimated center of Bakhmut. We were close enough to see smoke rising from the ruins of a nearby town. From the secret vantage point, Ukrainian soldier Izhak has kept a close eye on Russian positions in the distance.

"Our biggest fear is artillery," he said, "because it can hit us at any time. You don't know when, where, or how."

Russian regular forces and mercenaries from the Wagner group who've led the charge on Bakhmut have said they're close to encircling the charred and ruined city entirely. But the leader of the private Wagner army, Yevgeny Prigozhin, who's clashed in recent weeks with Shoigu and other top military brass over resources, said Monday that his forces needed backup and more ammunition.

"I'm knocking on all doors and sounding the alarm about ammunition and reinforcements, as well as the need to cover our flanks," Prigozhin said, highlighting a rift that may already have complicated Russia's bid to take Bakhmut.

"If everyone is coordinated, without ambition, screw-ups and tantrums, and carries out this work, then we will block the armed forces of Ukraine. If not, then everyone will be screwed," he said bluntly.

The strain on Russian troops as they're ordered to press the fight for Bakhmut against Ukrainian forces who've been promised backup from Kyiv and more weapons from Western partners has been made brutally clear as they're accused of committing horrific atrocities.

There has been a swell of international outrage this week over a gruesome video showing the apparent execution of a Ukrainian soldier by Russian forces around Bakhmut.

The Ukrainian soldier stands smoking a cigarette in a forest and is heard calmly issuing the refrain, "Glory to Ukraine," before a peel of gunfire appears to cut him down. A Russian voice, seemingly of one of the gunmen, is heard saying, "Die, b****."

Responding to the video — the latest evidence of alleged Russian war crimes in his country — Zelenskyy lauded the slain soldier Monday night, repeating his "glory to Ukraine" salute and vowing to "find the murderers."

In a Facebook post, the Ukrainian Armed Forces' 30th Mechanized Brigade identified the slain soldier as one of their own, naming him as Tymofiy Shadura. The post said he went missing amid fighting near Bakhmut on Feb. 3.  

Masik, a Ukrainian soldier who'd just returned from Bakmut, told CBS News that he and his fellow troops understood the risks and brutality of the battle to hold onto the city.

"Lots of us have been killed," he said. "But this is our land, and we must keep fighting."

While some military analysts have described Bakhmut as a largely symbolic battle over a city with little strategic value, Masik told CBS News its elevated topography, with the vantage point it offers to points further west, and its position on the road network, could partly explain why Russia has fought so hard to seize it. But he couldn't explain the seemingly first-world-war-tactic of just throwing more and more men at the front line to die.

"The Russians have said they've surrounded Bakhmut for half a year now," he said. "But we're here, on the edge of Bakhmut. Bakhmut will stand. Right now we have elite soldiers there who are repelling them, chewing them up… I think they're just throwing more forces at it to show they have achieved a goal - that there was some objective with this 'special operation.'"

"But they are falling in such high numbers, that I don't understand why. I can't explain why their commanders are ordering them to lay down so many lives with so little success," said Masik.

At a location nearby, deep in the woods, CBS News met members of a tank unit who had also experienced the horrors of the battle for Bakhmut first-hand. Vladyslav said his unit had fought on almost every front line of the war, and he didn't hesitate to call Bakhmut the "hottest" they'd seen.

Video captured the moment the tank he was driving took a direct hit from Russian fire.

"There was fire everywhere," he said. "People were walking around. I don't know how they live there - it was in ruins. At every step there were strikes."

He acknowledged his fear about the city falling to the Russian invaders.

"If the Russians take Bakhmut then Ukraine will be at a serious breaking point," he said. "It will be hard to get them out of there, and they will have many roads under control, so it will not be possible to bring supplies to our people."

But he was defiant.

"We are Ukrainians, and we need to get our land back, and we don't even talk about that," he said. "Bakhmut is holding. There is intense fighting, we were there. And I'll say it is scary, but it needs to be done."

In:
• War
• Ukraine
• Russia
• War Crimes
• Vladimir Putin
• Volodymyr Zelenskyy
• execution

Imtiaz Tyab

Imtiaz Tyab is a CBS News correspondent based in London.

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