WILLIAM BRANGHAM: Ukraine's president today visited near the site where two weeks ago his troops launched a surprise incursion into Russia.

Volodymyr Zelenskyy said Ukraine captured more territory and Russian soldiers in Russia's Kursk region.

Moscow said it foiled a Ukrainian attempt to seize land in the neighboring region of Bryansk.

And, meanwhile, Ukraine is continuing its efforts to bring the war into Russia using long-range drones.

Nick Schifrin has more.

NICK SCHIFRIN: In Southwest Russia today, a ferry carrying fuel for occupied Crimea went up in smoke, as did a Russian airfield 170 miles east of Ukraine's border.

Never before has Ukraine had so much long-range capacity to bring the war into Russia, which is what it continues to do on the ground in Kursk.

Ukrainian soldiers post videos attacking and trying to encircle Russian reinforcements.

They launch cluster munitions on bridges and makeshift crossings that Russians would need to use to redeploy.

Ukrainians are also digging in to try and hold territory that Kyiv calls a buffer zone.

The Russians in Kursk also appear ready for a long fight.

State TV showed new bomb shelters in the regional capital.

Ukraine controls about 450 square miles of Russian territory.

Russia said today it blocked two new Ukrainian incursions to the West.

But Kyiv hopes holding this territory can reduce attacks inside Ukraine and give Ukraine leverage in future peace talks, Ukrainian President Volodymyr Zelenskyy said today after his first visit here since the incursion.

VOLODYMYR ZELENSKYY, Ukrainian President (through translator): To drive the occupier from our land, we must create as many problems for the Russian state as possible on its own territory.

NICK SCHIFRIN: Russian President Vladimir Putin delivered his own analysis today, claiming Ukraine attacked a Russian nuclear power station.

Ukraine labeled that the pot calling the kettle black, since Russia two years ago seized Ukraine's Zaporizhzhia nuclear power plant.

And in Eastern Ukraine today, soldiers are struggling to prevent Russia from seizing more territory.

Russians have moved within six miles of Pokrovsk, a key Ukrainian logistics hub, whose capture could help Russia expand its control of the Donetsk region.

The fighting has been fierce and personal.

When a small Ukrainian drone approached a Russian soldier, he headbutted it and survived.

Both sides have hard heads when it comes to their missions.

DID, Ukrainian Army (through translator): We will stand here, kill them to the end, so that they do not go further, so they do not enter Pokrovsk.

They will not enter.

We will not let them.

NICK SCHIFRIN: But the Russians are advancing so quickly, today, much of Pokrovsk evacuated, including the most vulnerable.

Victoria carries her newborn to an unknown future, no idea if their home will remain Ukrainian.

VICTORIA, Ukraine Resident (through translator): It's so sad, I want to cry.

This is what I feel.

I don't want to go anywhere.

I want to be at home.

NICK SCHIFRIN: Home is where love resides.

And, today, love feels lost, many of their fathers forced to stay behind, forced to watch their sons through the window, forced to say goodbye, hoping it's not farewell.

Indian Prime Minister Narendra Modi will visit Kyiv tomorrow for the first time since the full-scale invasion.

He said today in neighboring Poland there should be a negotiated end to the war.

For more on Ukraine's incursion into Russia, Russia's advance in the east and the overall state of the war, we turn to Can Kasapoglu, senior fellow at the Hudson Institute.

Can Kasapoglu, thanks very much.

Welcome to the "News Hour."

We have now seen Ukraine say for the last two weeks that its goals in Kursk is to create a buffer zone and create some kind of leverage in future negotiations.

Is that a good strategy?

CAN KASAPOGLU, Senior Fellow, Hudson Institute: Well, actually, this is what they have as their best shot, because we have a very attritional war, and Russia has better stamina compared to Ukraine.

It is almost impossible to Ukraine to recapture the lost territory, especially given the scope of the Western military assistance.

So they had to go unconventional.

And this is the best unconventional shot that they could take.

And I think it is unfolding pretty well for Ukraine.

NICK SCHIFRIN: Can 450 square miles of Russian territory really give Ukraine leverage in any future peace talks?

CAN KASAPOGLU: Well, actually, it is not about the amount of territory.

It is about Ukraine when the music stops.

So it should be a dialogue between the equals and exchanging Russian territory in return for Ukrainian territory.

NICK SCHIFRIN: We saw earlier in my story Ukrainian soldiers digging in, obviously expecting some kind of Russian attempt to evict them.

Can they hold this territory?

CAN KASAPOGLU: Well, that's the million-dollar question.

The Ukrainian units need to do three things to pull it off.

First, they should dig in a very complex defensive architecture like the Russian strong points in the south that botched the Ukrainian offensive last year.

Second, this area should be under air defense umbrella of the Ukrainian military.

And, third, Ukrainian units shouldn't outrun their artillery and their rocket support.

NICK SCHIFRIN: U.S. and Ukrainian officials confirmed to me that they have not seen Russian soldiers reinforcing the lines in Kursk from the main areas of fighting in Eastern Ukraine, including Pokrovsk.

But U.S. officials confirmed to me also that Ukrainian forces pulled some of the soldiers, their own soldiers in Pokrovsk in order to invade in Kursk.

So what is the impact of this Kursk operation, could it have, on Ukraine's ability to hold in the east?

CAN KASAPOGLU: This was a gamble that Ukraine had to take, because, even if they amassed their troops in the Pokrovsk front, the operation wasn't going well for Kyiv.

And there is -- for a long time, Kyiv has been losing territory in the east inch by inch, day by day to the Russian incursion.

Both offensive campaigns have the good chance to go well.

And I wouldn't be surprised to see Ukrainians capitalizing on their gains and settling and digging in, in Kursk.

And that's -- and I wouldn't be surprised by seeing the Ukrainian flag in Kursk in the forthcoming months.

Likewise, I wouldn't be surprised to see the Russian combat formations fully invading Pokrovsk, Eastern Ukraine, in the forthcoming weeks or months.

NICK SCHIFRIN: What would be the impact if Russian forces did seize Pokrovsk?

CAN KASAPOGLU: Pokrovsk is the hub of transportation in the east, and that would open many options for the Russian military to capitalize on.

I think one direction that they might go is to further advance into Eastern Ukraine and complete the conquest of Donetsk region, which is the epicenter of the Russian military strategy in the east.

Russian military strategy in the east is very territorial.

NICK SCHIFRIN: And, finally, we have seen more and more long-range strikes, one on the Black Sea today, another at an air base deep into Russia, yesterday on Moscow itself.

What's the impact of Ukrainians being able to launch all these strikes?

CAN KASAPOGLU: At the geopolitical level, it is exposing Russia's nuclear bluff to the West.

We have seen this is not the first time that the Ukrainians are hitting deep Russian territory, and none of these attacks triggered a Russian tactical nuclear response.

That should tell something to the West.

Militarily, these strikes are important, because the Ukrainians are hitting Russian bases hosting aircraft and glide bombs.

The third thing that it is doing is that, along with the Kursk offensive, striking deep inside Russia is Ukraine's one and only option to show some offensive footing.

And it is also a calling to the West to lift all the caveats and restrictions over the Western military assistance for not to hit inside Russia, the Russian territory.

NICK SCHIFRIN: Can Kasapoglu, thank you very much.

CAN KASAPOGLU: Thank you.