Ukrainian authorities said they were trying to pull residents out of the frontline eastern city of Lysychansk, the focus of Russia's attacks where about 15,000 people remained under relentless shelling.
"Fighting is going on all the time. The Russians are constantly on the offensive. There is no let-up," regional Governor Serhiy Gaidai told Ukrainian television on Thursday.
"Absolutely everything is being shelled."
In the southern Kherson region, Ukrainian forces were fighting back with artillery strikes of their own, Oleskiy Arestovych, adviser to the Ukrainian president, said in a video posted online.
At a summit in Madrid on Wednesday, NATO invited Sweden and Finland to join and pledged a sevenfold increase from 2023 in combat forces on high alert along its eastern flank.
In reaction, President Vladimir Putin said Russia would respond in kind if NATO set up infrastructure in Finland and Sweden after they join the US-led military alliance.
Putin was quoted by Russian news agencies as saying he could not rule out that tensions would emerge in Moscow's relations with Helsinki and Stockholm over their joining NATO.
US President Joe Biden announced more land, sea and air force deployments across Europe from Spain in the west to Romania and Poland bordering Ukraine.
These included a permanent army headquarters with accompanying battalion in Poland, the first full-time US deployment on NATO's eastern fringes.
"President Putin's war against Ukraine has shattered peace in Europe and has created the biggest security crisis in Europe since the Second World War," NATO Secretary-General Jens Stoltenberg told a news conference.
"NATO has responded with strength and unity."
Britain said it would provide another Stg1 billion ($A1.8 billion) of military support to Ukraine, including air defence systems, uncrewed aerial vehicles and new electronic warfare equipment.
Russian forces intensified attacks in Ukraine, including missile strikes and shelling on the southern Mykolaiv region close to front lines and the Black Sea.
The mayor of Mykolaiv city said eight Russian missiles had struck and one had killed at least five people in a residential building, while Moscow said its forces had hit what it called a training base for foreign mercenaries in the region.
There was relentless fighting around the hilltop city of Lysychansk, which Russian forces are trying to encircle as they try to capture the industrialised eastern Donbas region on behalf of separatist proxies. Donbas comprises Donetsk and Luhansk provinces.
President Volodymyr Zelenskiy again told NATO that Ukrainian forces needed more weapons and money, and faster, to erode Russia's huge edge in artillery and missile firepower, and said Moscow's ambitions did not stop at Ukraine.
Russia says its February 24 invasion is a "special military operation" to rid Ukraine of dangerous nationalists. Ukraine and the West accuse Russia of an unprovoked, imperial-style land grab.
In a nod to the deterioration in relations with Russia since the invasion, a NATO communique called Russia the "most significant and direct threat to the allies' security", having previously classified it as a "strategic partner".
The new Strategic Concept document, NATO's first since 2010, said a "strong independent Ukraine is vital for the stability of the Euro-Atlantic area".
To that end, NATO agreed to a long-term financial and military aid package to modernise Ukraine's military.
"We stand in full solidarity with the government and the people of Ukraine in the heroic defence of their country," the communique said.
Stoltenberg said NATO had agreed to put 300,000 troops on high readiness from 2023, up from 40,000, under a new force model to protect an area stretching from the Baltic to the Black seas.
NATO's invitation to Sweden and Finland to join the alliance marks one of the most momentous shifts in European security in decades as Helsinki and Stockholm drop a tradition of neutrality in response to Russia's invasion.
