Ukrainian and Russian forces were fighting for "literally every meter" in Severodonetsk, President Volodymyr Zelensky said, as fighting intensified in an eastern region where the country's top commander said the land "is covered in blood".
Severodonetsk and nearby Lysychansk have been targeted for weeks as the last areas in the Lugansk region still under Ukrainian control, AFP said.
Russia's massed artillery in that region gave it a tenfold advantage, said Valeriy Zaluzhny, commander-in-chief of the Ukrainian military.
But, "despite everything, we continue to hold positions", he said.
"Every meter of Ukrainian land there is covered in blood -- but not only ours, but also the occupier's."
In his nightly video address, Zelensky said the latest fighting in Severodonetsk was "very fierce", adding that Russia was deploying undertrained troops and using its young men as "cannon fodder".
By attacking Severodonetsk's last remaining bridges, the Russians were aiming to cut the key industrial city off completely from the rest of the country, said regional governor Sergiy Gaiday.
"Most likely (in the next two days), they will throw all the reserves to capture the city," Gaiday said.
He also accused Russia of shelling the Azot chemical plant in Severodonetsk, where hundreds of civilians have reportedly taken refuge.
But Leonid Pasechnik, leader of Lugansk's pro-Russian separatists, pointed the finger at the Ukrainian battalions, saying they were the ones shelling Severodonetsk from the plant.
He told reporters that pro-Russian forces were not pressing aggressively "because it is a chemical industry facility", warning of the risk of "an environmental catastrophe".
- 'War crimes' -
Amnesty International on Monday accused Russia of war crimes in Ukraine, saying that attacks on the northeastern city of Kharkiv -- many using banned cluster bombs -- had killed hundreds of civilians.
"The repeated bombardments of residential neighborhoods in Kharkiv are indiscriminate attacks which killed and injured hundreds of civilians, and as such constitute war crimes," the rights group said in a report on Ukraine's second biggest city.
Away from the battlefield, World Trade Organization members gathered in Geneva Sunday, and at the top of the agenda was the issue of tackling global food security threatened by Russia's invasion of wheat-producing Ukraine.
Tensions ran high during a closed-door session, where several delegates took the floor to condemn Russia's war, including Kyiv's envoy who was met with a standing ovation, WTO spokesman Dan Pruzin told journalists.
Then, just before Russian Minister of Economic Development Maxim Reshetnikov spoke, around three dozen delegates "walked out", the spokesman said.
That came a day after the head of the European Commission promised Ukraine would receive a clear signal within a week on its bid to join the European Union.
EU leaders are expected to approve the bid at an upcoming summit, although with strict conditions attached.
In Brussels, demonstrators brandishing blue and yellow Ukrainian flags circled European Commission headquarters Sunday in a show of support.
- Chortkiv strike -
The war has prompted Finland and Sweden to give up decades of military non-alignment and seek to join the NATO alliance.
But Turkey is blocking their bids and NATO chief Jens Stoltenberg said Sunday the issue may not be resolved by an alliance summit later this month.
The United States and Europe have sent weapons and cash to help Ukraine blunt Russia's advance, alongside punishing Moscow with unprecedented economic sanctions.
Russian forces said Sunday they had struck a site in the town of Chortkiv in western Ukraine storing US- and EU-supplied weapons.
Russia's defense ministry said the strike destroyed a "large depot of anti-tank missile systems, portable air defense systems and shells provided to the Kyiv regime by the US and European countries".
The strike -- a rare attack by Russia in the relatively calm west of Ukraine -- left 22 people injured, regional governor Volodymyr Trush said.
He added that four missiles fired Saturday evening from the Black Sea had partially destroyed a military installation in the town, about 140 kilometers (85 miles) from the border with Romania.
Concerns eased Sunday over Ukraine's largest nuclear power plant in Zaporizhzhia. Captured months ago by Russian forces but still operated by Ukrainians, the station had ceased transmitting vital safeguards data two weeks ago.
But plant officials working with the International Atomic Energy Agency have succeeded in restoring transmission, the IAEA said.
Rafael Grossi, director general of the UN agency, said it still wanted to send inspectors to the plant "as soon as possible".
- Sentences defended -
Alongside the physical fighting, the war is being played out through the courts.
Pro-Moscow separatist authorities in the Donetsk region this week sentenced to death two Britons and a Moroccan for fighting with the Ukrainian army.
The sentences sparked outrage in Western countries, but separatist Donetsk leader Denis Pushilin said Sunday he would not alter them.
"They came to Ukraine to kill civilians for money," he told reporters, calling the punishment "perfectly fair".
The families of Britons Aiden Aslin and Shaun Pinner say they have been living in Ukraine since 2018.
Ukrainian courts have handed three Russian soldiers long prison sentences at war crimes trials.