Russian troops keep pushing forward in waves along the frontline in eastern Ukraine, Ukrainian soldiers said on Tuesday, as President Vladimir Putin reaffirmed his view that Russia's very existence as a state was at stake in the war. In the eastern Donbas region, Russia and Ukraine are locked in the bloodiest infantry battle in Europe since World War Two after Moscow launched a winter offensive. Putin has framed Moscow's year-long war invasion as a defensive pushback against what he sees as a hostile West bent on expanding into territories historically ruled by Russia. "So for us this is not a geopolitical task, but a task of the survival of Russian statehood, creating conditions for the future development of the country and our children," he said during a visit to an aviation factory in Buryatia, some 4,400 km (2,750 miles) east of Moscow. Putin accuses the West of using Ukraine as a tool to inflict "strategic defeat" on Russia. Kyiv and its Western allies say Moscow is waging an unprovoked war of conquest that has destroyed Ukrainian cities, killed thousands of people and forced millions more to flee their homes. Frontlines have barely budged in more than four months of Russia's winter offensive despite huge losses on both sides. With assaults elsewhere on the front having failed, Russia appears determined to secure the ruins of the small city of Bakhmut in what would be its first victory since mid-2022. ‘Very painful’ In a video address, President Volodymyr Zelenskiy said Ukraine's "future is being decided" in battles in the east, including Bakhmut, where Ukrainian commanders say they are killing enough Russian attackers to justify staying and fighting for a wrecked city that has nearly been surrounded. "It is very tough in the east - very painful," Zelenskiy said. "We have to destroy the enemy's military power. And we shall destroy it." Zelenskiy and his military chiefs agreed on Tuesday to keep defending Bakhmut despite concerns among some military analysts that the losses Ukraine is suffering could undermine its ability to mount a planned counter-offensive when the weather improves. "It is key to the stability of the defense of the entire front," said General Valeriy Zaluzhnyi, Commander-in-Chief of the Ukrainian Armed Forces, praising his soldiers' fortitude. Further north on the frontline near Kreminna, Oleksandr, 50, commander of a unit in Ukraine's 110th battalion, said Russian assaults were still relentless despite having claimed little ground there. The Russians are trying to edge back towards Lyman, a transit hub Ukraine recaptured last year. "They are pushing hard. They are lobbing mortar bombs at us," Oleksandr told Reuters, describing Russian units advancing in three-man fire teams, with another wave behind them sent to replace them when they are killed. "At night they always attack on foot and we sit, looking through our thermal goggles, and shooting them." The Kremlin, for its part, said Kyiv must accept "new realities" - its shorthand for Russia's claim to have annexed nearly a fifth of Ukraine. "We have to achieve our goals. Right now this is only possible by military means due to the current position of the Kyiv regime," Russian state news agencies quoted Kremlin spokesman Dmitry Peskov as saying. Denis Pushilin, the administrator of Russian-controlled parts of Ukraine's Donetsk region, said battles for "every meter" of Bakhmut were taking place. "We can see that the Ukrainian regime absolutely does not take into account the numerous losses in the (Ukrainian town of) Soledar and the direction of Bakhmut. In fact, with its orders, it grinds down its own soldiers," Pushilin was quoted as saying by the RIA news agency. Shell shortage After recapturing swathes of territory in the second half of 2022, Kyiv has kept mainly to the defensive over the past four months, while Moscow has launched its winter offensive using freshly mobilized reservists and convicts recruited from jail as mercenaries. Britain's Ministry of Defense said on Tuesday Moscow was running short of ammunition, "to the extent that extremely punitive shell-rationing is in force on many parts of the front". "This has almost certainly been a key reason why no Russian formation has recently been able to generate operationally significant offensive action," it said in a daily intelligence update. But Ukraine is also facing shortages of shells, and ultimately has a smaller population to commit to a battle of attrition. Both sides reported more civilian casualties near the front. Zelenskiy said six high-rise buildings were hit in the center of Kramatorsk by a Russian missile, killing at least one person and wounding three. On the Russian-occupied side, in Volnovakha further south, the body of a woman lay on a street next to a ruined shop. A Russian military investigator told Reuters the area was hit by Ukrainian shells. Two civilians were also killed and one injured in Russian artillery shelling of two villages in the Kharkiv region in northeast Ukraine, regional prosecutors said. Off the battlefield, negotiators hit a snag in talks to extend the Black Sea grain deal, brokered by the United Nations and Turkey to prevent global famine by securing wartime exports from Ukraine and Russia, both among the world's top food suppliers. The agreement expires this week. Russia said it had agreed to let it be extended for 60 days, in what the Kremlin called a gesture of "goodwill", but would block any further extension unless it received more guarantees from the West for exports of its own fertilizer and crops. Kyiv rejected the 60-day extension, saying the agreement allows extensions only of 120 days. It says a shorter duration would not be long enough to organize new grain shipments.