AMNA NAWAZ: In year three of Russia's full-scale invasion of Ukraine, Kyiv has, over the last week, flipped the script on Moscow with an audacious incursion into southern Russia, catching Moscow by surprise and sowing chaos.

GEOFF BENNETT: Today, Ukraine said it had blasted its way deeper into the Kursk region of Russia, where it has captured dozens of towns and settlements and taken Russians prisoner.

And the governor of the neighboring Belgorod region declared a state of emergency.

It is the largest cross-border attack since Russia's full-scale invasion and the largest presence of foreign troops in Russia since World War II.

Here's Nick Schifrin.

NICK SCHIFRIN: For nearly two-and-a-half years, Ukraine has struggled on defense.

Today, it's on offense.

For the past week, Ukrainian soldiers have thrown aside Russian President Vladimir Putin's claim the war wouldn't touch Russia.

They have trampled through more than 70 Russian villages, raising Ukrainian flags over small-town administrative buildings and changing Russian spellings into Ukrainian.

The incursion has reached about 18 miles into Russia, what Ukraine says is about 390 square miles.

Ukrainian soldiers show off their operation with video selfies, playing and driving heavy metal.

They advance through territory thinly defended.

But there's been a fight.

Ukrainians pulled the flags off Russian soldiers' helmets they just killed by the side of the road.

And Russian soldiers have been captured and driven back into Ukraine, what President Volodymyr Zelenskyy calls an exchange fund.

VOLODYMYR ZELENSKYY, Ukrainian President (through translator): We have proven once again that we Ukrainians are capable of achieving our goals in any situation, capable of defending our interests and our independence.

NICK SCHIFRIN: Ukraine says this is not an occupation, but its soldiers posted videos in control of a gas facility, even picking up provisions from a Russian grocery store.

None of this territory is particularly important militarily, but the image of Ukrainian soldiers patrolling Russian villages, many emptied after the evacuation of 75,000 residents, is a shock to Russians and a boost to Ukrainian pride and this state TV reporter.

In Moscow, Putin hosted a public forum this week with governors and cut off the Kursk governor as he detailed the size of Ukraine's incursion.

VLADIMIR PUTIN, Russian President (through translator): Alexei, the military will report to us what the width and depth are there.

You tell us about the socioeconomic situation and report on assistance to people.

NICK SCHIFRIN: To try and evict Ukrainian soldiers from Russia, U.S. and Ukrainian officials confirmed that Russia has redeployed some soldiers from inside Ukraine to aid the defense.

But Ukraine had its own redeployment.

U.S. officials confirmed at least some of the soldiers who crossed the border into Russia left the Pokrovsk region, where they were fending off heavy Russian attacks.

Ukraine is also trying to bring the fight into Russia with long-range drones.

Today, Ukraine said it had launched its largest drone strike yet deep into Russia.

One target was this Russian air base before and after the strike.

To discuss the incursion into Kursk and the overall state of the war, we turn to Michael Kofman, senior fellow in the Russia and Eurasia Program at the Carnegie Endowment for International Peace, a think tank in Washington, D.C. Michael Kofman, thanks very much.

Welcome back to the "News Hour."

What's significance does this incursion have, do you believe, on the wider war?

MICHAEL KOFMAN, Carnegie Endowment for International Peace: Nick, it's a very significant development and it's already significantly lifted the morale of Ukrainian troops and changed the prevailing narrative, which is that the war has been on a negative trajectory.

But we're still fairly on into the Ukrainian operation.

This incursion has been going on for over a week.

And it's clearly a fairly sizable operation, in terms of the forces that the Ukrainian military has committed.

And they met with initial success and were able to break through Russian forces early on when they entered Kursk.

NICK SCHIFRIN: So let me -- we will go into the military details of what's happening in Kursk, but let me just ask strategically also what's the political impact on President Putin himself or the overall narrative that comes out of the Kremlin?

MICHAEL KOFMAN: Well, obviously, the incursion into Kursk with the Ukrainian forces now being on Russian territory is deeply embarrassing for the Kremlin.

And even though the Russian military is still continuing to try to advance across the front line in Ukraine, Kursk now is front and center stage, and it's, of course, going to change the external perceptions of many of the other countries looking at this war.

I think Russian leadership was trying to portray a huge degree of confidence prior to the Ukrainian offensive, thinking that there was essentially maybe no way they could lose.

But this has the potential to really change potentially their perspectives and those of others.

NICK SCHIFRIN: So, zooming back into Kursk, why do you believe the Ukrainians have had some success?

Why was this area apparently so thinly defended?

MICHAEL KOFMAN: So it's clear that the Russian leadership didn't anticipate an attack across the border into their own territory.

The Ukrainian military first encountered border guards who were surprised and Russian conscripts who weren't well-prepared or equipped to fight them.

And after the initial breakthrough, they had to some extent the run of the place for the first couple of days.

The Russian military has taken a long time to deploy reserves to the area.

And, typically, Russian military does not do well in a very dynamic situation.

NICK SCHIFRIN: So what are the Russian military reserves who are there trying to do, presumably stop the Ukrainians?

But Putin will have to evict these Ukrainians.

How difficult will that be?

MICHAEL KOFMAN: Well, first, it's still not clear what the goal of the Ukrainian military operation is.

I think they hope that Russian military will divert a lot of their forces from their current offensive in Ukraine in order to try to counter this incursion.

So far, the Russian military has pulled some forces from the front line in Ukraine.

Unfortunately, it's not the areas where they were conducting offensives.

Those are still ongoing.

Now, the Ukraine advance has slowed down significantly after the first couple of days, although it is still making progress.

The Russian military is trying to counter it and trying to stabilize the front.

They still have not been able to do that.

The Ukrainian military is pouring more forces into this operation and taking more troops off of the front lines in Ukraine in order to try to push and expand in the Kursk region.

NICK SCHIFRIN: On the flip side, as I reported earlier, Ukraine itself decided to redeploy some of its troops from Ukraine, including around the Pokrovsk area, where it's fighting quite pitched battles with Russia, move them into Russia.

Is there any risk to Ukraine's effort inside its own country?

MICHAEL KOFMAN: So there is a risk.

An operation like this actually comes with significant risk of overextension.

The Ukrainian military took some of its better troops, thinned out its defensive lines in Donetsk, other parts of the country, in order to conduct this operation.

Ukraine does not have a substantial advantage in reserves or manpower.

Now, there is an upshot, and it's clear that they can achieve some significant gains potentially.

But there is also significant downside and risk.

With thinned-out lines, the Russian military is making advances towards Pokrovsk and the other parts of Ukraine.

And a lot depends on what happens both in Kursk and in the coming days with Russian force deployment.

So, if the Russian military is able to stabilize this offensive without having to pull a substantial amount of forces from their operations in the rest of Ukraine, then this offensive might end up being a lot less successful than initially hoped for.

It still remains to be seen.

NICK SCHIFRIN: A U.S. official confirms to me that Ukraine is using American weapons systems inside of Russia.

How significant is that?

MICHAEL KOFMAN: So it's good Ukraine is operating Western equipment, Western vehicles, and has even been conducting HIMARS strikes inside the Kursk region against Russian reserves.

And it seems to have basically a degree of tacit acceptance, if not support, from Western countries to do that.

I think it's a notable development, since Ukraine has been for a long time pushing for exchange in policy and a greater tolerance and essentially greater freedom to be able to employ Western equipment and Western capabilities, not just in defense of its own territory, but in being able to take the fight to Russia.

NICK SCHIFRIN: And finally, Michael Kofman, I mentioned before what Ukraine called its largest long-range drone strike into Russia, hitting four Russian airfields.

How significant are these long-range drone strikes that Ukraine is able to do now that it wasn't able to do at the beginning of the war?

MICHAEL KOFMAN: It's a notable development, because Russia has had the advantage in long-range strike capability attacking Ukrainian infrastructure for the better part of this war.

But over the past year, Ukraine has significantly increased its production of long-range strike drones, has been concentrating them in these types of strikes and ensuring that actually it may now hold the advantage not in overall strike capabilities, certainly not compared to the number of cruise missiles the Russian military can fire, but compared to the number of drones that the Russian forces use.

Ukraine is starting to steadily overtake them in the size of overall strikes and is only set to expand those types of attacks in Russia, essentially retaliating and having a degree of ability to inflict damage on Russian air bases or Russian infrastructure.

NICK SCHIFRIN: Michael Kofman, thanks very much.

MICHAEL KOFMAN: Thanks for having me.