Last week, in the first case of its kind linked to the Ukraine Troops Hold Out as Russia Assaults Sievierodonetsk Wasteland
Both sides said Russian forces now controlled between a third and half of the city. Russia's separatist proxies acknowledged that capturing it was taking longer than hoped, despite one of the biggest ground assaults of the war.
Western military analysts say Moscow has drained manpower and firepower from across the rest of the front to concentrate on Sievierodonetsk, hoping a massive offensive on the small industrial city will deliver something Russia can call a victory in one of its stated aims in the east.
"We can say already that a third of Sievierodonetsk is already under our control," Russia's TASS state news agency quoted Leonid Pasechnik, the leader of the pro-Moscow Luhansk People's Republic, as saying.
Fighting was raging in the city, but Russian forces were not advancing as rapidly as might have been hoped, he said, claiming that pro-Moscow forces wanted to "maintain the city's infrastructure" and were moving slowly because of caution around chemical factories.
The Ukrainian head of the city administration, Oleksandr Stryuk, said the Russians now controlled half of the city.
"Unfortunately ... the city has been split in half. But at the same time the city still defends itself. It is still Ukrainian," he said, advising those still trapped inside to stay in cellars.
Ukraine says Russia has destroyed all of the city's critical infrastructure with unrelenting bombardment, followed by wave after wave of mass ground assault involving huge numbers of casualties.
Thousands of residents remain trapped. Russian forces are advancing towards the city center, but slowly, and have not succeeded in encircling the Ukrainian defenders holding out there.
Regional governor Serhiy Gaidai told Ukrainian television there did not appear to be a risk of Ukrainian forces being encircled, though they could ultimately be forced to retreat across the Siverskiy Donets river to Lysychansk, the twin city on the opposite bank.
Stryuk, head of the city administration, said evacuating civilians was no longer possible. Authorities canceled efforts to evacuate residents after an attack on Monday that killed a French journalist.
Jan Egeland, secretary general of the Norwegian Refugee Council aid agency which had long operated out of Sievierodonetsk, said he was "horrified" by its destruction.
"We fear that up to 12,000 civilians remain caught in crossfire in the city, without sufficient access to water, food, medicine or electricity. The near-constant bombardment is forcing civilians to seek refuge in bomb shelters and basements, with only few precious opportunities for those trying to escape."
Elsewhere on the battlefield, there were few reports of major action on Tuesday. In the east, Ukraine says Moscow is trying to assault other areas along the main front, including pressing towards the city of Solviansk. In the south, Ukraine claimed in recent days to have pushed back Russian forces on a bank of the Inhulets River that forms a border of Russian-held Kherson province.
After having failed to capture Kyiv, been driven out of northern Ukraine and made only limited progress elsewhere in the east, Moscow has concentrated the full force of its armed might in recent days on Sievierodonetsk, which had a pre-war population of around 110,000.
Victory there and in adjoining Lysychansk would let Moscow claim control of Luhansk province, one of two eastern regions it claims on behalf of separatist proxies, partly achieving one of President Vladimir Putin's stated war aims.
But the huge battle has come at a massive cost, which some Western military experts say could hurt Russia's ability to fend off eventual Ukrainian counterattacks elsewhere, regardless of who wins the battle for Sievierodonetsk.
"Putin is now hurling men and munitions at the last remaining major population center in (Luhansk), Sievierodonetsk, as if taking it would win the war for the Kremlin. He is wrong," the Washington-based Institute for the Study of War think tank wrote this week.
"When the Battle of Severodonetsk ends, regardless of which side holds the city, the Russian offensive at the operational and strategic levels will likely have culminated, giving Ukraine the chance to restart its operational-level counteroffensives to push Russian forces back."
The EU on Monday agreed its toughest sanctions against Russia since the war began, for the first time targeting Russian sales of oil, by far Moscow's main source of income.
The EU will now ban import of Russian oil by sea. Officials said that would halt two-thirds of Russia's oil exports to Europe at once, and 90% by the end of this year as Germany and Poland also phase out imports by pipeline.
Hungary, which relies on Russian oil through a huge Soviet-era pipeline, secured an exemption, though EU officials said they expected this would be "temporary."
Ukraine says the sanctions are taking too long and are still too full of holes to stop Russia: "If you ask me, I would say far too slow, far too late and definitely not enough," said Ihor Zhovkva, deputy head of President Volodymyr Zelenskiy's office.
Moscow, meanwhile, has switched off gas supplies to several EU countries in a dispute over how to receive payments, although the moves so far, during warm months when demand is lower, have yet to have the severest impact. On Tuesday, Russia switched off the main Dutch gas buyer, GasTerra, which said it would find supplies elsewhere.
Putin launched his invasion of Ukraine in February claiming Moscow aimed to disarm and "denazify" its neighbor. Ukraine and its Western allies call this a baseless pretext for a war to seize territory.