AMNA NAWAZ: Russia says that it's fighting raids by Ukrainian forces for a second straight day inside Russia's border.

The intense battles are said to be taking place in the Kursk region, across from the Ukrainian region of Sumy.

It appears to be one of the largest incursions into Russian territory since Russia's full-scale invasion of Ukraine two-and-a-half years ago.

The Ukrainian government has not claimed responsibility for or acknowledged the attack.

Ukraine has been trying to intensify its fight against Russia not only across the 800-mile front line, but also in territory that Russia has occupied since 2014, Crimea.

And that is where Ukraine is achieving some success.

Here's Nick Schifrin with more.

NICK SCHIFRIN: In a war where Ukraine struggles to hold the line, Ukraine boasts with highly produced videos a theater of success, Russian-occupied crime era, where Russian boats have gone up in smoke.

Ukraine has zero warships, but Kyiv and Washington say Ukrainian sea drones have destroyed more than a dozen Russian ships.

And now Ukraine has unleashed on Crimea its most powerful American weapon, the Army Tactical Missile System, or ATACMS.

A U.S. official tells "PBS News Hour" the U.S. has sent Ukraine hundreds of missiles, each with a range of nearly 190 miles and a price tag of $1.3 million.

JAKE SULLIVAN, U.S. National Security Adviser: I'm announcing an emergency package of security assistance of $300 million.

NICK SCHIFRIN: After lengthy internal debate and external pressure, the administration first authorized ATACMS for Ukraine in mid-March.

And U.S. officials say Ukraine first used them in mid-April, this strike on a Russian airfield in occupied Crimea.

LT. GEN. BEN HODGES (RET.

), U.S. Army: ATACMS help Ukraine achieve the goal of making the Crimean Peninsula uninhabitable for Russian army, navy and air force.

NICK SCHIFRIN: Retired Lieutenant General Ben Hodges is the former commander of U.S. Army Europe.

He's long argued the road to Ukrainian victory runs through Crimea, whose 2014 annexation is one of President Vladimir Putin's crowning achievements and where the Russian military has expanded ever since.

LT. GEN. BEN HODGES: Now Ukraine has enough ATACMS to be able to hit all the airfields, every ship that's in Sevastopol and the harbor and other important facilities.

That's the goal, make that place untenable for Russian forces.

NICK SCHIFRIN: U.S. officials confirm attack ATACMS helped sink a Russian submarine last weekend and have damaged or destroyed Russian airfields and at least a dozen Russian air defense batteries in Crimea, including some of Russia's most advanced, S-300s and S-400s, and among the warships, the Tsyklon, one of the first sunk by a ballistic missile.

Ukraine's attacks help force Russia's most valuable naval assets out of Crimea into Southern Russia, a feat first accomplished with long-range British Storm Shadow missiles that Ukraine has been launching since last year.

LT. GEN. BEN HODGES: These hits matter a lot, partly because of the fact that the Russians cannot replace them.

Crimea is a launching pad of all sorts of different missiles, rockets, drones that are hitting civilian infrastructure.

The ability to do that has been significantly reduced.

NICK SCHIFRIN: These tactical gains help advance a strategic goal, keep Ukrainian commerce flowing through the Black Sea.

Ukraine's food exports now match or even exceed levels from before the full-scale invasion.

That income is critical to keep Ukraine's government afloat so it can pay soldiers' salaries and to Ukraine's long-term half-a-trillion-dollar reconstruction.

VOLODYMYR ZELENSKYY, Ukrainian President (through translator): Over the course of this war, Ukraine has gained an entirely new status in the Black Sea.

This region will now always be free from Russian dominance.

NICK SCHIFRIN: The U.S. and Ukraine also say ATACMS could challenge Russian supply lines into Crimea, including via ferry.

U.S. officials confirm ATACMS damaged two ferries that Russia uses to move fuel and ammunition, and Ukraine destroyed the third.

Those strikes penetrated one of the most fortified air defenses on the planet around the Kerch Bridge, which connects Crimea to mainland Russia.

Ukraine set it ablaze in October 2022 with an improvised explosive device that Russia said was equivalent to 10 tons of TNT.

In December 2022, Putin took a drive to reassure Russians the bridge was solid.

In July 2023, the Ukrainian sea drone hit it again.

But U.S. officials confirm that Russia has shot down ATACMS, including in late June, when shrapnel from a shot-down missile that was aimed at a military target instead rained down on beachgoers.

Russian media showed sun loungers used as stretchers, and Russian officials said the strike killed at least four people, including children, and wounded 150 more.

If the U.S. and Ukraine want Crimeans to feel unsafe, tourists told local journalists it's working.

MAN (through translator): We hope for the best, but, of course, deep inside, we have a sense of danger.

NICK SCHIFRIN: But the biggest danger to Ukraine exists far from Crimea.

In the east, Ukraine has struggled to hold the line after shortages of manpower and munitions.

Some experts question whether Crimea is the most vital front for an American weapon in relatively short supply.

ANATOL LIEVEN, Director of the Eurasia Program, Quincy Institute: This is of great significance, but it doesn't critically affect the overall future of the war.

NICK SCHIFRIN: Anatol Lieven directs the Quincy Institute's Eurasia Program.

He says the ATACMS would be better saved for an expected Russian offensive.

ANATOL LIEVEN: There is therefore a case for the Ukrainians conserving their ATACMS and other weapons and ammunition for that moment.

NICK SCHIFRIN: Ukraine also wants to use ATACMS elsewhere, inside Russia, especially on bases with planes that drop devastating 2,000-pound bombs, but the U.S. restricts ATACMS use to inside Ukraine.

VOLODYMYR ZELENSKYY: We can protect our cities from Russian guided bombs if American leadership makes a step forward and allows us to destroy Russian military aircrafts on their bases.

NICK SCHIFRIN: But until the U.S. takes that step, Crimea is a concentrated target and an example of Ukrainian success in a war of attrition with no end in sight.

For the PBS "News Hour," I'm Nick Schifrin.