Ukrainian President Volodymyr Zelensky has said the key city of Lyman is now "completely cleared" of Russian troops.

The town in the country's east is located in one of the four Ukrainian regions that Russia annexed.

"As of 12.30pm (9.30am Irish time) Lyman is completely cleared, thank you to our military!" Mr Zelensky said in a video posted on social media.

There was no comment from the Russian armed forces on the status of the city.

The Russian defence ministry said yesterday that it was pulling troops out of the area "in connection with the creation of a threat of encirclement".

The latest stinging setback for Russian President Vladimir Putin came after he proclaimed the annexation of four regions covering nearly a fifth of Ukraine on Friday, an area that includes Lyman.

Kyiv and the West have condemned the proclamation as an illegitimate farce.

Russian forces captured Lyman from Ukraine in May and had used it as a logistics and transport hub for its operations in the north of the Donetsk region. Losing it is Russia's largest battlefield loss since Ukraine's lightning counteroffensive in the northeastern Kharkiv region last month.

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Serhiy Gaidai, governor of the Luhansk region that neighbours Donetsk, said control over Lyman could help Ukrainere claim lost territory in his region, whose full capture Moscow announced in early July after weeks of grinding advances.

"The liberation of this city in the Donetsk region is one of the key factors for the further de-occupation of the Luhansk region," Mr Gaidai wrote on the Telegram messaging app this morning.

Mr Zelensky yesterday promised more quick successes in the Donbas, which covers the Donetsk and Luhansk regions that are largely under Russian control.

"Over the past week, the number of Ukrainian flags in Donbas has increased. There will be even more a week's time," Mr Zelensky said in an evening address.

The areas Mr Putin claimed as annexed - the Donbas regions and the southern regions of Kherson and Zaporizhzhia - form a swathe of territory equal to about 18% of Ukraine's total surface land area.

The battlefield setbacks have triggered a fresh wave of criticism within Russia of how its military operation is being handled.

Putin ally Ramzan Kadyrov, the leader of Russia's southern Chechnya region, called for a change of strategy "right up to the declaration of martial law in the border areas and the use of low-yield nuclear weapons."

Other top officials, including former president Dmitry Medvedev, have suggested Russia may need to resort to nuclear weapons, but Mr Kadyrov's call was the most urgent and explicit.

Washington says it would respond decisively to any use of nuclear weapons.

US Defense Secretary Lloyd Austin said Lyman's capture would create new problems for Russia's military.

"We're very encouraged by what we're seeing right now,"Austin told a news conference.

He noted that Lyman was positioned across supply lines that Russia has used to push its troops and material down to the south and to the west, as the Kremlin presses its more than seven-month-long invasion of Ukraine.

"Without those routes, it will be more difficult. So it presents a sort of a dilemma for the Russians going forward.

A destroyed bridge leading to Lyman

Ukraine's armed forces said in a statement this morning that its jets had carried out 29 strikes in the last 24 hours, destroying weapons and anti-aircraft missile systems, while ground troops had hit command posts, warehouses containing ammunition and anti-aircraft missile complexes.

Russian forces launched four missiles and 16 air strikes and used Iranian-made "Shahed-136" drones to attack infrastructure, Ukraine's statement said, adding more than 30 settlements were damaged, chiefly in the south and southeast.

Reuters could not verify either side's battlefield assertions.

A man walks past abandoned Russian tanks in Kramatorsk, eastern Ukraine

Analysts at the Institute for the Study of War (ISW), a Washington-based think tank, said the Russian military in its current state is almost certainly unable to operate on a nuclear battlefield even though it has historically trained its units to do so.

"The chaotic agglomeration of exhausted contract soldiers, hastily mobilised reservists, conscripts, and mercenaries that currently comprise the Russian ground forces could not function in a nuclear environment. Any areas affected by Russian tactical nuclear weapons would thus be impassable for the Russians, likely precluding Russian advances," ISW said.

Serhii Cherevatyi, spokesperson for Ukraine's eastern forces, said before its capture that Russia had 5,000 to 5,500 troops at Lyman, but the number encircled could be lower.

Ukraine says taking Lyman will allow it to advance into the Luhansk region, whose full capture Moscow announced in early July after weeks of grinding advances.

"Lyman is important because it is the next step towards the liberation of the Ukrainian Donbas," Mr Cherevatyi said.

"It is an opportunity to go further to Kreminna and Sievierodonetsk, and it is psychologically very important."

The Donbas has been a major focus for Russia since it launched the invasion on 24 February that Mr Putin calls a "special military operation" to demilitarise and "denazify" its smaller neighbour.

The areas he claimed as Russian - the Donbas regions of Donetsk and Luhansk and the southern regions of Kherson and Zaporizhzhia - form a swathe of territory equal to about 18% of Ukraine's total surface land area.

Germany, meanhwhile, has said it will deliver the first of four advanced IRIS-T air defence systems to Ukraine in coming days to help ward off drone attacks.