AMNA NAWAZ: Russian forces claim to have conquered the city of Bakhmut than Ukraine's east.

Kyiv denied that and said the nine-month battle for the city continues.

Meantime a force of pro-Ukrainian troops who say their Russians made an incursion into a Russian border region.

Stephanie Sy reports.

STEPHANIE SY: In Bakhmut, Russian soldiers walked through a city they destroyed and now claim they have conquered.

A brutal nine-month battle has devastated the 400-year-old city, which had a prewar population of more than 70,000 people.

Russian state media showed these soldiers raising the Russian flag in the ruins of the city, next to it, the flag of the Wagner mercenary group, which led the assault.

MAN (through translator): Without exaggeration, this is a historic moment.

This is it.

There are no more houses.

The city has been taken.

STEPHANIE SY: The Wagner Group was founded by Yevgeny Prigozhin, a convicted Russian criminal and Kremlin-connected businessman who over the weekend claimed victory.

YEVGENY PRIGOZHIN, Wagner Group Chief (through translator): Thanks to Vladimir Vladimirovich Putin for giving us the high honor to defend our motherland.

We fought not only with the Ukrainian armed forces in Bakhmut, but also with the Russian bureaucracy.

STEPHANIE SY: Earlier this month, Prigozhin threatened to withdraw his troops from the city, accusing Russian military officials of withholding ammunition and blaming them for the death of Wagner fighters.

YEVGENY PRIGOZHIN (through translator): We have a 70 percent shortage of ammunition.

Shoigu, Gerasimov, where is the ammunition?

Look at them.

STEPHANIE SY: But President Vladimir Putin yesterday praised the private military group.

Ukrainian officials say the battle for Bakhmut is not over and that its soldiers continue to advance from the north and south to encircle Russian troops inside the city.

At the G7 meeting over the weekend, President Volodymyr Zelenskyy compared the city to Hiroshima after the U.S. dropped an atomic bomb on it in World War II.

VOLODYMYR ZELENSKYY, Ukrainian President: But you have to understand that there is nothing.

They destroyed everything.

There are no buildings.

It's a pity.

It's tragedy, but, for today, Bakhmut is only in our hearts.

STEPHANIE SY: Today, in another development, a group of anti-Putin Russian defectors claimed on social media videos to have crossed into Russian territory and liberated parts of the border region of Belgorod.

MAN (through translator): We are Russians just like you.

We are people just like you.

We want our children to grow up in peace and be free people.

But this has no place in today's Putin's Russia.

STEPHANIE SY: The so-called Liberty of Russia Legion says their end goal is to end Putin's dictatorship.

Joining us now to discuss what is going on in Bakhmut and other developments as Dara Massicot.

She is a senior policy researcher at the RAND Corporation.

Dara, thank you for joining the "NewsHour."

So what is going on in Bakhmut?

Can the Russians claim victory, or is this still going on?

DARA MASSICOT, RAND Corporation: Well, the Russians are claiming victory.They occupy a large percentage of what remains of the city.

Most of Bakhmut is destroyed right now.

Ukraine still occupies areas on the heights not too far away from the city.

And they are claiming that they're putting pressure on the Russian flanks.

I think it's safe to say that Russia probably has most of the city at this point.

There's perhaps one or two roads that lead out that the Ukrainians still -- they still have.

Russia is desperate for a win.

And this is just about the only win that they can come up with after a failed offensive.

STEPHANIE SY: I keep hearing that Bakhmut is not particularly strategically significant in this war.

So why have nine months of such a hard-fought battle continued?

DARA MASSICOT: Well, the Ukrainian armed forces have really prioritized this area and their desire to keep it has been very strong.

Russia has also fought very hard for it using conscripts, mobilized forces from Wagner, I mean, and suffered a lot of casualties.

If Russia is able to capitalize on taking Bakhmut and pressing forward, it does open up a significant road network.

But what I'm seeing is an exhausted force that is not able to move forward.

STEPHANIE SY: The Ukrainians are still claiming that they have encircled at least a part of the city.

So if the Russians really have taken it over, is it your sense that they could hold a Bakhmut?

Or would that continue to be a challenge with Ukrainian forces on the outside flanks?

DARA MASSICOT: So, Ukraine is saying that they are pressuring the north and the south of Bakhmut, and they're causing some localized retreats from Russian forces that are there, I can't independently corroborate that they have encircled the actual city, but they are putting pressure on those units.

And those are not high-speed units.

They're made of mobilized or they come from proxy forces, so it might be easier to disrupt them than other units that are farther back.

STEPHANIE SY: So how big of a cost it has this battle been to Russian forces, especially as we talk about the potential for a Ukrainian counteroffensive this spring?

DARA MASSICOT: The Russians have paid a heavy price for a counteroffensive for not much gains.

It comes from the way that they're fighting this war.

And, in some places, they're using storm troops, more human wave-style assaults on Ukrainian positions.

And it's coming at a high price.

I think it's probably inevitable that Russia is going to have to do another round of mobilization this year to replace the casualties.

STEPHANIE SY: I want to ask you about another development that's been reported today.

And that is that Russian defectors who are now anti-Putin, and they call themselves the Freedom of Russia Legion, claimed to have crossed the border from Ukraine into Russia, and claimed to have -- quote - - "liberated" parts of the Belgorod region, which is on the border of Ukraine and Russia.

How significant is that?

And what does it mean for them to have liberated parts of Belgorod?

DARA MASSICOT: This is a really interesting story and it's still developing.

But this is essentially a group that is affiliated loosely with the Ukrainian military, but it's not aligned with a Ukrainian military unit by any stretch.

They were actually able to move well inside Russia.

And the Russian authorities have confirmed that this is happening.

It looks like, from Twitter, that -- Russian Telegram, that they managed to steal a vehicle from the Russian border guards.

So this is a very embarrassing situation for Russia.

They're trying to spin their way out of it right now, claiming that this is Ukrainian diversionary tactics for losing Bakhmut.

But this is really a black eye and an embarrassment for the Russians.

STEPHANIE SY: Putin seems to be treating buck mode like it's Stalingrad, like it's going to change the tide of the war.

Is that your sense that, if the Russian forces have indeed captured this city, that it would somehow turn the direction of the war?

DARA MASSICOT: No, I think that he's trying to spin whatever victory that he can come up with to show for the Russian people, for the amount of casualties that they have lost.

They have had basically no successes over the past four or five months, if not longer than that, frankly.

And this is the best that they can come up with to spin it.

I don't think that it's going to give them a strategic advantage this year.

The force is simply too exhausted to try to forward again in a meaningful way.

I don't think they have the capability for another large offensive this year.

STEPHANIE SY: Dara Massicot with the RAND Corporation, thanks so much for joining the "NewsHour."

DARA MASSICOT: Thank you for having me.