Ukrainian forces were successfully holding out against the assault in Sievierodonetsk, the general staff said on Wednesday, while Russian troops were bringing in new resources towards Donbas in an intense battle for control of the eastern region.
The days-long battle for the industrial city has emerged as pivotal, with Russia focusing its offensive might in the hope of achieving one of its stated aims - to fully capture surrounding Luhansk province on behalf of Russian-speaking separatists.
"The absolutely heroic defence of Donbas is ongoing," Ukrainian President Volodymyr Zelenskiy said in a video statement on Tuesday. Sievierodonetsk, Lysychansk, and Popasna, remain the most difficult places, he added.
"It is absolutely felt that the occupiers didn't believe the resistance of our military would be so strong and now they are trying to bring in new resources towards the Donbas," he said.
Reuters could not independently verify the situation on the ground.
Since being pushed back from Kyiv and Kharkiv, Russia has focused on the region known as the Donbas, comprised of Luhansk and Donetsk provinces, and closest to the Russian border.
Moscow says it is engaged in a "special military operation" to disarm and "denazify" its neighbour.
Ukraine and allies call this a baseless pretext for a war that has killed thousands, flattened cities and forced millions of people to flee. Zelenskiy said Ukraine would launch next week a "Book of Executioners" to detail war crimes.
"These are concrete facts about concrete individuals guilty of concrete cruel crimes against Ukrainians," he said.
Russia says it has gone out of its way to avoid targeting civilians in its operation in Ukraine.
Satellite imagery from Maxar Technologies collected on Monday showed significant damage in Sievierodonetsk and nearby Rubizhne.
"Our soldiers are successfully holding back the assault in the city of Sievierodonetsk," the Ukraine general staff said on Wednesday, adding its troops were also holding off attacks in Toshkivka and Ustynivka to the south.
Reuters could not immediately verify the reports.
Luhansk Governor Serhiy Gaidai said on Wednesday that Lysychansk, which is across the river from Sievierodonetsk, was also being shelled. A local man was killed on a central street on Tuesday and a woman was hospitalised, he added.
In Sloviansk, about 85 km (53 miles) to the west of Sievierodonetsk, women with small children lined up to collect aid on Tuesday while other residents carried buckets of water across the city as they prepared for advancing Russian forces.
"I am going to remain, I will not leave without my husband. He works here. That's what we decided, we are staying," said Irina, who did not provide her surname, as she waited with a child in a stroller outside an aid distribution centre.
"It is tough, but it is easier when one is at home."
Ukraine's second city, Kharkiv, was also hit by shelling on Tuesday, and the local mayor said one person was killed. The northeastern city had been quieter in recent weeks.
Viacheslav Shulga, an employee at a pizzeria in the north of Kharkiv that was hit, said there had been hopes the restaurant could reopen soon.
"Everything is destroyed. We are removing equipment, there will be no business here for now," he said.
More than two weeks since a siege of the southern city of Mariupol ended, Tass news agency cited a Russian law enforcement source as saying that over 1,000 Ukrainian soldiers who surrendered there have been transferred to Russia for investigation.
As the effects of the war are felt around the world, the United States added further sanctions to Moscow by banning U.S. money managers from buying any Russian debt or stocks in secondary markets.
The World Bank approved $1.49 billion in fresh funds to help pay wages for government and social workers in Ukraine as it and other countries deal with the damage to its economy.
Ukraine is one of the world's biggest exporters of grain, and Western countries accuse Russia of creating the risk of global famine by shutting Ukraine's Black Sea ports.
Russian attacks on agricultural sites in the Mykolaiv region were compounding a world-wide food crisis, Ukraine's southern military command said on Facebook on Wednesday.
"Those who pretend to be concerned about the world food crisis are in fact attacking farmland and infrastructure sites where fires of considerable scale have broken out," it said.
The governor of the region that includes the port of Mykolaiv said weekend shelling had destroyed warehouses in one of Ukraine's largest agricultural commodities terminals.
Moscow denies responsibility for the international food crisis, blaming Western sanctions.
Russian Defence Minister Sergei Shoigu said the Russian-occupied Ukrainian ports of Berdyansk and Mariupol were ready to resume grain exports. Ukraine says any such shipments from territory seized by Moscow would amount to illegal looting.
(Reporting by Reuters; Writing by Himani Sarkar; Editing by Michael Perry)