Ukraine's troops move cautiously into Kherson as Russia declares its hasty withdrawal complete

Russia's military said on Friday that it had completed its withdrawal from the southern Ukrainian city of Kherson, the only regional capital that Vladimir Putin's invading army had managed to capture since he launched his full-scale war at the end of February. The military said "not a single piece of military equipment" was left on the western bank of the Dnipro River, which bisects the wider Kherson region, with the city of the same name sitting on its west bank.

In a statement, military commanders in Moscow said "all Russian servicemen crossed" the river without sustaining "losses of personnel, weapons, military equipment and material." The announcement came just two days after Russia's defense chief ordered the retreat from Kherson city, with his top commander in Ukraine telling him in a televised conversation that it was "not easy" to make the call, but that it would "save the lives of our military."

There was no immediate word from Ukrainian or U.S. military officials to confirm the Russian announcement, but Ukrainian lawmaker Oleksiy Goncharenko told CBS News correspondent Chris Livesay that his country's forces were in the city of Kherson on Friday morning. He had said earlier in a tweet that Ukrainian troops were "already in Kherson."

Images quickly emerged on social media showing Ukraine's national flag flying in front of the regional administration building. Videos showed civilians hugging Ukrainian soldiers and helping them hang Ukrainian flags on other buildings, including the city's police headquarters.

There were claims by Ukrainian civilians on social media that some Russian troops had put on civilian clothes and remained behind, and Ukrainian troops were entering cautiously, wary of mines and boobytraps. 

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Ukrainian and U.S. officials were skeptical of the Russian withdrawal announcement from the moment it was issued on Wednesday, suggesting it could be a trap to lure Ukraine's forces eastward, toward entrenched Russian positions on the eastern bank of the Dnipro.

As of Thursday evening in Ukraine, U.S. officials told CBS News they had seen no signs of Russian troops moving in significant numbers across the river. CBS News national security correspondent David Martin said that wasn't necessarily viewed as evidence that the withdrawal announcement was a ruse, just that it would likely take time.

While there was no official confirmation of the status of the Russian withdrawal from Ukrainian commanders, unverified videos posted online showed what appeared to be Russian troops crossing a pontoon bridge across the Dnipro on foot. The bridge sat right next to the larger Antonivskiy Bridge, which multiple videos showed completely unusable, with a large section destroyed.

While it wasn't immediately clear what caused the collapse of the road bridge, BBC News reported that the key piece of infrastructure had been "gradually damaged by Ukrainian missiles" during Russia's months-long occupation of Kherson city and much of the surrounding region.

Russia's invading forces have suffered setbacks for the last couple months, retreating from towns and villages west of Kherson, and in areas north of that region, amid a Ukrainian counteroffensive bolstered by the huge influx of Western weapons.

While the Ukrainian advance has pushed the Russians back quickly, the U.S. has been reluctant to grant country's requests for even more advanced weapons systems, and many analysts expect the rapid shift in the front lines of the last couple months to slow as winter sets in and Russia entrenches in positions it has held for years further in eastern Ukraine.

Ukrainian soldiers just a few miles from enemy lines have been using Western-supplied drones to hone in on Russian positions. But the Russians can also see the Ukrainians coming.

Russia's relatively new commander in the war — dubbed "General Armageddon" — has shown he is willing to use devastating tactics, relying on long-range missile and drone strikes to pummel civilian areas in a bid to decrease Ukrainian morale.

The strikes have knocked out power and water supplies to millions of Ukrainians, and as CBS News correspondent Chris Livesay reports, Russia's retreating forces have also left behind them a deadly trail of landmines and boobytraps.

Even if and when Ukraine does confirm that Russia's forces have pulled out of Kherson, the Russian threat, with its indiscriminate firepower, will still lie entrenched just across the river. And despite mounting calls for peace talks, there's little to suggest the war that has raged for more than eight months, and simmered for more than eight years before that, is about to end.

So far, U.S. officials estimate the war has claimed the lives of roughly 40,000 Ukrainian civilians, while some 100,000 of the country's forces have been killed or injured. Russian forces are believed to have sustained a similar number of casualties. 

CBS News producer Erin Lyall contributed to this report.

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• Vladimir Putin