Ukrainian forces were still holding out inside Severodonetsk and trying to evacuate civilians, authorities said on Tuesday, after Russia destroyed the last bridge to the devastated eastern city in a potential turning point in one of the war's bloodiest battles.

"The situation is very difficult but there is communication with the city" despite the last bridge over the Severskyi Donets river having been destroyed, said the Ukrainian Mayor of Severodonetsk Oleksandr Stryuk. "Russian troops are trying to storm the city, but the military is holding firm," he claimed.

"The city is not isolated," Stryuk told Ukrainian television. "There are communication channels even if they are quite complicated," he added.

He also said Ukrainian troops "continue to defend the city" and that there is round-the-clock fighting, adding that the situation on the ground "changes every hour."

Ukraine says more than 500 civilians are trapped inside a chemical factory in an industrial zone of the city where its forces have resisted weeks of Russian bombardment and assault.

Evacuations were still being carried out "every minute when there is a lull and there is a possibility of transportation," Stryuk said. "But these are discrete evacuations, done one by one, and every possible chance is taken," he explained.

Both sides claim to have inflicted huge casualties in the fighting over the city, Russia's main target in its battle for the east after it failed to capture Ukraine's capital Kyiv in March.

Ukraine still holds Lysychansk, Severodonetsk's twin city on higher ground on the opposite bank. But with all the bridges now cut, its forces acknowledge a risk they could be encircled if they remain. Russia's separatist proxies said any Ukrainian troops left behind must surrender or die.

Damien Megrou, spokesperson for a unit of foreign volunteers helping to defend Severodonetsk, said there was a risk of leaving "a large pocket of Ukrainian defenders cut off from the rest of the Ukrainian troops" – as in Mariupol, which fell in May after months of Russian siege.

During the fall of Mariupol last month, hundreds of civilians and badly wounded Ukrainian soldiers were trapped for weeks in the Azovstal steelworks.

'Most brutal battle'

The battle for Severodonetsk – a city of barely more than 100,000 people before the war – is now the biggest fight in Ukraine as the conflict has shifted into a punishing war of attrition.

Kyiv has said it is losing a staggering 100-200 soldiers killed each day, with hundreds more wounded. In an overnight address, President Volodymyr Zelenskyy described the battle for the eastern Donbass region as one of the most brutal in European history.

Zelenskyy on Monday said the battle for Severodonetsk was taking a "terrifying" toll as Russian forces threaten to take the strategic eastern city.

"The human cost of this battle is very high for us. It is simply terrifying," he added.

Russia gives no regular figures of its own losses but Western countries say they have been massive, as Moscow has committed the bulk of its firepower to delivering one of President Vladimir Putin's stated objectives: Forcing Kyiv to cede the full territory of two eastern provinces.

Momentum in Severodonetsk has shifted several times over the past few weeks – with Russia concentrating its overwhelming artillery firepower on urban districts to obliterate resistance, then sending in footsoldiers vulnerable to counterattacks.

Bigger battles could lie ahead for the wider Ukrainian-held pocket of the Donbass, nearly all on the opposite bank of the river that Russian forces have found difficult to cross. Ukraine says Russia is massing to assault Sloviansk from the north and along a front near Bakhmut to the south.

It has pleaded for the West to send more and better artillery to neutralize Russia's main advantage. Ukraine needs 1,000 howitzers, 500 tanks and 1,000 drones among other heavy weapons, Presidential Adviser Mykhailo Podolyak said on Monday.

Western countries have promised NATO-standard weapons – including advanced U.S. rockets. But deploying them is taking time, and meanwhile Ukraine is running out of ammunition for its existing Soviet-era arsenal, which is dwarfed by Russia's.

Beyond the Donbass, Ukrainian officials hope that Russia's focus on capturing the east will drain its forces from other areas, paving the way potentially for counterattacks to recapture other territory.

It recaptured the area around its second largest city Kharkiv in May and has reported small but steady gains in recent days in the south, the biggest swath Russia still retains of the territory it seized after its invasion in February.

Serhiy Khlan, adviser to the head of the southern, mainly Russian-occupied Kherson province, said Ukraine was having tactical success recapturing territory there for a second straight week. Troops had already advanced 5 kilometers (3.11 miles) from Tavriysk, a town on the south bank of the Dnipro river east of Kherson city, and were gradually advancing, he said.

"We have tactical victories. They are turning into a counteroffensive. For the counteroffensive, we are waiting for the reinforcement of equipment from our partners," Khlan said.

Officials in the Russian-backed separatist-controlled Donetsk region said at least three people, including a child, were killed and 18 were wounded by Ukrainian shelling that hit a market in Donetsk city.