KYIV, UKRAINE -- Military authorities in the eastern Ukrainian city of Pokrovsk urged civilians to speed up their evacuation Friday because the Russian army was quickly closing in on what has been one of Moscow's key targets for months.

Pokrovsk officials said in a Telegram post that Russian troops are "advancing at a fast pace. With every passing day there is less and less time to collect personal belongings and leave for safer regions."

Ukrainian troops have been trying to divert the Kremlin's military focus away from the front line in Ukraine by launching a bold cross-border incursion into Russia's Kursk region. But Ukrainian President Volodymyr Zelenskyy warned Thursday that Pokrovsk and other nearby towns in the Donetsk region were "facing the most intense Russian assaults."

An aerial reconnaissance soldier with Ukraine's 68th Separate Airborne Brigade who is helping defend the city told The Associated Press by phone on Friday that he faces the same deadly monotony every day: From his position, he flies a drone to identify moving Russian infantrymen. The boom of a mortar follows after he relays the coordinates. Then, more and more infantrymen come in a seemingly endless wave.

"Since the Kursk operation, I haven't noticed any changes. The Russians have the same tactics of infantry assaults: They are moving, advancing," said the soldier, who gave only his call sign, Goose, in keeping with Ukrainian military rules.

He noted that with their powerful aerial bombs, Russia was destroying any hope Ukrainians have of holding the territory. "Russians are destroying and moving, destroying and moving," Goose said.

The urgency of the evacuation of civilians from Pokrovsk has underscored the high-stakes gamble Ukraine is making by taking the war into Russia with its ongoing Kursk assault, which started Aug. 6.

The attack is a daring attempt to change the dynamics of the two-and-a-half-year conflict, but it could backfire and leave Ukraine's shorthanded defence on the front line at the mercy of Russia's push. The Kremlin's forces have had battlefield momentum and superior forces in eastern Ukraine's Donetsk region since the spring.

Ukraine is wagering it can cope with the strain on its resources involved in the attack in Kursk without sacrificing Donetsk. Russia apparently reckons it can contain the incursion without needing to ease up in Donetsk.

"Both cannot be right," Nigel Gould-Davies, a senior fellow at the International Institute for Strategic Studies, said Thursday. "The outcome hangs in the balance."

The United States does not believe Ukraine can control the territory seized in Kursk over the long term, said a U.S. official who spoke on condition of anonymity because they were not authorized to comment publicly on the matter.

The official said that the Russians have yet to deploy a significant number of troops away from Ukraine and into the Kursk to try to repel the Ukrainian operation. But American officials believe such a redeployment or a surge of Russian forces from elsewhere will inevitably happen and likely be able to fend off the Ukraine forces, the official said.

Russia's slow slog across Donetsk this year has been costly in terms of troops and armour, but its gains have mounted.

Pokrovsk, which had a prewar population of about 60,000, is one of Ukraine's main defensive strongholds and a key logistics hub in the Donetsk region. Its capture would compromise Ukraine's defensive abilities and supply routes, and would bring Russia closer to its stated aim of capturing the entire Donetsk region.

Pokrovsk officials were meeting with the residents to provide them with logistical details on the evacuation. People were offered shelter in western Ukraine, where they will be hosted in dormitories and separate houses prepared for them.

"As the front line approaches Pokrovsk, the need to move to a safer place is becoming increasingly urgent," the local administration said.

In Kursk, meanwhile, Ukraine's top military officer, Gen. Oleksandr Syrskyi, said Friday that Ukrainian troops had advanced one to three kilometres (up to two miles) deeper into Russian territory. He claimed earlier this week that Ukraine controlled more than 1,000 square kilometres (390 square miles) inside Russia, but Moscow disputes the claim and it couldn't be independently verified.

Syrskyi also said Ukraine continues to capture Russian soldiers during the incursion as an "exchange fund" of captives to be swapped for Ukrainian prisoners of war, though it remains unclear how many have been captured. On Wednesday, Ukraine's human rights chief, Dmytro Lubinets, said he spoke with his Russian counterpart, Tatyana Moskalkova, about a possible POW swap.

On Friday, the AP visited a detention center in Ukraine, the location of which cannot be disclosed due to security restrictions. Dozens of POWs were seen, some of them walking with their hands tied behind their backs while a guard led them down a corridor. Some had rations of a thin soup with cabbage and onions.

According to the facility's officials, more than 300 captives have passed through it since the start of the incursion, with 80 per cent of them being conscripts.

Russian President Vladimir Putin has repeatedly stated that conscripts would not participate in the "special military operation," Russia's term for its war against Ukraine. However, because of the speed of Ukraine's incursion, the war came to them.

Ukrainian troops have taken full control of Sudzha, Zelenskyy said Thursday. It's the largest Russian town to fall to Ukraine's forces since the start of their incursion 10 days ago, and the success raised Ukrainian spirits while embarrassing the Kremlin.

A family who fled from Sudzha showed on Russian state TV the shattered windows of their car, the result of an attack while on the road.

"At the turn they were shooting, there were mines, we drove around the mines. Then we were driving further, the drone hit us in Bondarevka," said Nikolai Netbayev.

The Russian Defence Ministry said Friday the army repelled attempted Ukrainian advances in the areas of Gordeev, about 25 kilometres (15 miles) west of Sudzha, and Russkoye Porechnoye, 13 kilometres (eight miles) north of Sudzha.

In other developments, the Russian organization People's Front said two of its volunteer workers were killed by Ukrainian shelling in the Kursk region while on a mission to evacuate residents.

And in the Russian-occupied city of Donetsk, a hypermarket was destroyed in a blaze after being hit by Ukrainian fire, according to local officials. Eleven people were reported injured.

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Hatton reported from Lisbon, Portugal. Associated Press reporters Samya Kullab and Volodymyr Yurchuk in Kyiv, Alex Babenko and Evgeniy Maloletka in Ukraine, Jim Heintz in Tallinn, Estonia, and Aamer Madhani in Washington contributed.