Ukrainian and Russian forces are battling on the outskirts of Sievierodonetsk, in Ukraine's Luhansk province, as European Union countries failed to agree on a Russian oil import ban.
Russian shelling has reduced much of the city to ruins but the Ukrainian defence has slowed the wider Russian campaign across the Donbas region.
Luhansk region governor Serhiy Gaidai said Russian troops had advanced into Sievierodonetsk's southeastern and northeastern fringes.
"They use the same tactics over and over again. They shell for several hours - for three, four, five hours - in a row and then attack," Gaidai said.
"Those who attack die. Then shelling and attack follow again, and so on until they break through somewhere."
He said that with temperatures rising, there was a "terrible smell of death" on the city outskirts.
But Ukrainian forces had driven the Russian troops out of the village of Toshkivka to the south, he said, potentially frustrating Russia's push to encircle the area.
As the battlefield struggle ground on, EU countries meeting in Brussels to discuss more sanctions failed to agree on a ban of Russian oil imports despite last-minute haggling before a summit.
The EU has rolled out five packages of sanctions against Russia since its troops invaded Ukraine on February 24 but an agreement on oil sanctions has proved elusive because so many countries depend on Russian crude.
"There is no compromise for this moment at all," Hungarian Prime Minister Viktor Orban said.
His country has been the main holdout for a deal.
Ukrainian President Volodymyr Zelenskiy questioned the lack of EU resolve.
"Why are you dependent on Russia, on their pressure, and not vice-versa? Russia must be dependent on you. Why can Russia still earn almost a billion euros a day by selling energy?" he said in an address to EU leaders.
"Why are terrorist banks still working with Europe and the global financial system? Serious questions."
President Vladimir Putin meanwhile said that Russia was ready to facilitate grain exports from Ukrainian ports - a possibility that could alleviate a food crisis as the war and the sanctions to isolate Russia have sent the price of grain and other commodities soaring.
Russia says the focus of what it calls its "special military operation" is now to seize the entire Donbas region, consisting of two provinces, Luhansk and Donetsk, that it claims on behalf of separatist proxies.
Russian Foreign Minister Sergei Lavrov said on Sunday the "liberation" of Donbas was an "unconditional priority".
Capturing Sievierodonetsk and its twin city Lysychansk on the opposite bank of the Siverskyi Donets river would give Russia effective control of Luhansk and would allow the Kremlin to declare some form of victory after more than three months of death and destruction.
Ukraine says its forces pushed back Russian troops in recent days to defensive positions in three villages - Andriyivka, Lozove and Bilohorka - all on the south bank of the Inhulets River that forms the border of Kherson.
A French journalist, Frederic Leclerc-Imhoff of television channel BFM, was killed near Sievierodonetsk on Monday when shelling hit the vehicle he was travelling in as civilians were allowed to leave the area.
French Foreign Minister Catherine Colonna, who was visiting Ukraine at the time, demanded an investigation.
In the Netherlands, GasTerra, which buys and trades gas on behalf of the Dutch government, said it would no longer receive gas from Russia's Gazprom from Tuesday after refusing to agree to Russia's demands for payment in roubles.
US and European leaders have blamed Russia for holding the world to ransom by blockading Ukrainian ports and the United Nations, which says a global food crisis is deepening, is trying to broker a deal to unblock Ukraine's grain exports.
Putin, in talks with Turkish President Tayyip Erdogan, said Russia was ready to facilitate the unhindered export of grain from Ukrainian ports in co-ordination with Turkey, the Kremlin said.
"Emphasis was placed on ensuring safe navigation in the Black and Azov seas and eliminating the mine threat in their waters," the Kremlin said of Putin's call with Erdogan.
Putin also said that if sanctions were lifted, then Russia could export significant volumes of fertilisers and agricultural products.
Australian Associated Press
