President Volodymyr Zelensky said Ukrainian forces were "holding on" in the flashpoint eastern city Severodonetsk where intense street battles with Russian troops could determine the fate of the Donbas region.
Moscow has concentrated its firepower on the industrial city, which it now mostly controls, with the area's governor saying on Friday that Russian forces had destroyed a major sports arena.
Pro-Russian rebels sentenced one Moroccan and two British fighters to death on Thursday after they were captured while fighting for Ukraine and accused of acting as mercenaries for Kyiv.
Zelensky said in his evening address on Thursday night that several "cities in Donbas, which the occupiers now consider key targets, are holding on".
He added that Ukrainian forces have made positive strides in the Zaporizhzhia and Kharkiv regions, and are in the process of "liberating our land".
With the fiercest fighting now concentrated in Severodonetsk, governor Sergiy Gaiday -- who earlier called for Western artillery to quickly help secure a Ukrainian victory -- said "one of the symbols of Severodonetsk was destroyed. The Ice Palace burned down".
Western countries have provided weapons and aid for Ukraine since the February 24 invasion, while several people from abroad have joined the fight against Russian forces.
Up to 100 Ukrainian soldiers were being killed every day in frontline fighting and as many as 500 wounded, Defence Minister Oleksiy Reznikov said.
- Death sentence -
Separatist authorities in the Donetsk region of the Donbas ordered the death penalty for Aiden Aslin, Shaun Pinner and Saadun Brahim, Russian media reported.
Britain's Foreign Secretary Liz Truss called the sentence "a sham judgment with absolutely no legitimacy".
A spokesman for Prime Minister Boris Johnson said the sentence contravenes the Geneva Convention, under which "prisoners of war are entitled to combatant immunity".
Britons Aslin and Pinner surrendered in April in the southern port city Mariupol, which was captured by Russian troops after a weeks-long siege. They later appeared on Russian TV calling on Johnson to negotiate their release.
Moroccan Brahim surrendered in March in the eastern town of Volnovakha.
During a trial that lasted three days, the men pleaded guilty to committing "actions aimed at seizing power and overthrowing the constitutional order of the Donetsk People's Republic", Russian news agency Interfax said.
A lawyer representing one of them told the TASS news agency that they would appeal.
- 'Foreign mercenaries' -
After being repelled from Kyiv weeks into their invasion, Russian President Vladimir Putin's troops have refocused their offensive on the eastern Donbas.
Pro-Russian separatists have held part of the region since 2014.
Moscow, which has repeatedly warned the West against getting involved, said it had targeted a Ukrainian training centre for "foreign mercenaries" in the Zhytomyr region, west of Kyiv.
The Ukrainian presidency said four people were killed in a Russian air strike on Toshkivka, a village around 25 kilometres (16 miles) south of Severodonetsk.
It reported seven other deaths in fighting across the country.
In Kyiv, Ukraine's Interior Minister Denys Monastyrsky said the capital was in no immediate danger, but troops were keeping a line of defence all the same.
Putin, meanwhile, appeared to compare his actions to Peter the Great's conquest of the Baltic coast during his 18th-century war against Sweden.
"By fighting Sweden he was grabbing something... He was taking it back," he told young entrepreneurs in Moscow.
"It is our responsibility also to take back and strengthen".
- 'Every day something burns' -
Zelensky on Thursday called for Russia to be expelled from the UN's Food and Agriculture Organization (FAO), blaming Moscow for "causing hunger" and spurring the global grain crisis by invading his country.
Ukraine's Black Sea ports export millions of tonnes of grain each year but have been blocked since the invasion, while western sanctions on Russia have prevented Moscow from selling much of its grain abroad, sending food prices soaring.
The FAO warned that poor countries will suffer the most from the crisis as they were "paying more but receiving less food".
Africa has been hard hit by the shortage, and the African Union (AU) on Thursday urged Kyiv to demine waters around the Ukraine-controlled Odessa port to ease exports, warning of "serious famine" and destabilisation on the continent.
Moscow has also called for Ukraine to demine, but Kyiv has refused for fear of a Russian attack.