In his daily address late Tuesday, Ukrainian president Volodymyr Zelensky had struck a defiant tone: "The absolutely heroic defence of Donbas continues."
Russia's offensive is now targeting the Donbas region, which includes Lugansk and Donetsk, after its forces were pushed back from Kyiv and other areas following the February invasion.
The cities of Severodonetsk and Lysychansk, which are separated by a river, are the last areas still under Ukrainian control in Lugansk.
The war's impact continued to reverberate, with the World Bank cutting its global growth estimate to 2.9 percent -- 1.2 percentage points below the January forecast -- due largely to the invasion of Ukraine.
The toxic combination of weak growth and rising prices could trigger widespread suffering in dozens of poorer countries still struggling to recover from the upheaval of the Covid-19 pandemic, the bank said.
"The risk from stagflation is considerable with potentially destabilising consequences for low and middle income economies," World Bank president David Malpass told reporters.
"For many countries recession will be hard to avoid," Malpass said.
The bank additionally announced $1.5 billion more in aid for Ukraine, bringing the total planned support package to more than $4 billion.
Lavrov in Turkey
Amid stark warnings of global food shortages partly blamed on the war, Russian Foreign Minister Sergei Lavrov is set to meet Wednesday with his Turkish counterpart Mevlut Cavusoglu during a visit to Ankara.
Talks will focus on efforts to open a security corridor to ship Ukrainian grain -- cereals and wheat in particular -- stuck in the war-torn country's ports due to a Russian blockade.
"Right now we have about 20-25 million tonnes blocked. In the autumn that could be 70-75 million tonnes," Zelensky said Monday.
At the request of the United Nations, Turkey has offered its services to escort maritime convoys from Ukrainian ports, despite the presence of mines -- some of which have been detected near the Turkish coast.
Both sides accuse one another of destroying agricultural areas, which could worsen global food shortages.
"Those who pretend to be concerned about the global food crisis are, in fact, hitting agricultural fields and infrastructure, where fires are breaking out on an impressive scale," the Ukrainian military said Tuesday, pointing to attacks in the southern city of Mykolaiv.
'Bombings every day'
Severodonetsk appeared close to being captured just days ago but Ukrainian forces launched counterattacks and managed to hold out, despite warnings they are outnumbered by superior forces.
Lanny Davis, a US lawyer for Ukraine tycoon Dmytro Firtash, said 800 civilians had taken refuge in the bunkers inside Firtash's huge Azot chemical plant in the city.
The situation was also increasingly desperate in Lysychansk.
"Every day there are bombings and every day something burns. A house, a flat... And there is nobody to help me," 70-year-old Yuriy Krasnikov told AFP.
"I tried to go to the city authorities, but nobody's there, everyone has run away."
Ivan Sosnin was among some residents who decided to stay despite the Russian offensive.
"This is our home, that's all we know. We grew up here, where else should we go?" said the 19-year-old.
The leader of Ukraine's pro-Russian separatists in Donetsk, Denis Pushilin, on Tuesday confirmed the death of another Russian general in the fighting.
Pushilin expressed on Telegram his "sincere condolences to the family and friends" of Major General Roman Kutuzov, "who showed by example how to serve the fatherland".
Ukraine's forces have claimed to have killed several of Russia's top brass but their exact number is not known as Moscow is tight-lipped on losses.
On Tuesday, Zelensky announced the launch next week of a "Book of Torturers", a system that will collect details of alleged war crimes and Russian soldiers accused of committing them.
"I have repeatedly stressed that they will all be held accountable. And we are approaching this step by step," he said.
"Everyone will be brought to justice."