NATO estimated on Wednesday that 7,000 to 15,000 Russian soldiers have been killed in four weeks of fighting in Ukraine. A large number of casualties came to be as the country"s defenders have put up stiffer-than-expected resistance and denied Moscow the lightning victory it hoped for. A senior NATO military official said the estimate was based on information from Ukrainian officials, what Russia has released — intentionally or not — and intelligence gathered from open sources. The official spoke on the condition of anonymity under ground rules set by NATO. Russia has not given an official update since it said on March 2 that 498 soldiers had been killed in action in Ukraine. The pro-Kremlin Komsomolskaya Pravda newspaper, citing the Defence Ministry, briefly reported Monday that almost 10,000 Russian soldiers had been killed. The report was quickly removed, and newspaper blamed hackers. When Russia unleashed Europe’s biggest offensive since World War II on 24 February and brandished the prospect of nuclear escalation if the West intervened, a swift toppling of Ukraine’s democratically elected government seemed likely. But with Wednesday marking four full weeks of fighting, Russia is bogged down in a grinding military campaign, with untold numbers of dead, no immediate end in sight, and its economy crippled by Western sanctions. Despite plenty of evidence to the contrary, Kremlin spokesman Dmitry Peskov insisted the military operation was going “strictly in accordance" with plans. Russia wants to “get rid of the military potential of Ukraine” and “ensure that Ukraine changes from an anti-Russian center to a neutral country,” Peskov said. Officially, Russia is calling the campaign a “special military operation”. It has effectively outlawed terms such as “invasion” and “war,” and police have arrested thousands of antiwar protesters. But as casualties mount and quick victory is no longer in sight, Russia is having to work to shore up morale. Western officials say that Putin"s forces are facing serious shortages of food, fuel and cold weather gear. “We have seen indications that the Ukrainians are going a bit more on the offensive now,” Pentagon spokesman John Kirby said. He said that was particularly true in southern Ukraine, including near Kherson. But Russia’s far stronger, bigger military has many Western experts warning against overconfidence in Ukraine’s long-term odds. The Kremlin"s practice in past wars has been to grind down resistance with strikes that flattened cities, killing countless civilians and sending millions fleeing. Major Russian objectives remain unfulfilled. The capital, Kyiv, has been shelled repeatedly hit but is not even encircled. More shelling and gunfire shook the city Wednesday, with plumes of black smoke rising from the western outskirts, where the two sides battled for control of multiple suburbs. Mayor Vitali Klitschko said at least 264 civilians have been killed in the capital since the war broke out. In the south, the port city of Mariupol has seen the worst devastation of the war, under weeks of siege and bombardment. But Ukrainian forces have prevented its fall, thwarting an apparent bid by Moscow to fully secure a land bridge from Russia to Crimea, seized from Ukraine in 2014. Addressing Japan’s parliament on Wednesday, Ukrainian President Volodymyr Zelenskyy said four weeks of war have killed thousands, including at least 121 of Ukraine"s children. “Our people cannot even adequately bury their murdered relatives, friends and neighbors. They have to be buried right in the yards of destroyed buildings, next to the roads,” he said. Repeatedly pushed back by hit-and-run Ukrainian units armed with Western-supplied weapons, Russian troops are shelling targets from afar, falling back on tactics they used in reducing cities to ruins in Syria and Chechnya. Zelenskyy said 100,000 civilians remain in Mariupol, a city of 430,000 people. It has been shattered by strikes from air, land and sea, and repeated efforts to get desperately needed food and other supplies to those trapped have often failed. “They bombed us for the past 20 days,” said 39-year-old Viktoria Totsen, who fled from Mariupol to Poland. “During the last five days, the planes were flying over us every five seconds and dropped bombs everywhere — on residential buildings, kindergartens, art schools, everywhere.” Zelenskyy, speaking Tuesday in his nightly video address to his nation, said efforts to establish humanitarian corridors for the residents of the southern port city are almost all being “foiled by the Russian occupiers, by shelling or deliberate terror”. He accused Russian forces of seizing one humanitarian convoy. Deputy Prime Minister Iryna Vereshchuk said the Russians were holding captive 11 bus drivers and four rescue workers along with their vehicles. It is not clear how much of Mariupol is still under Ukrainian control. Fleeing residents say fighting continues street by street. In their last update, over a week ago, Mariupol officials said at least 2,300 people had died, but the true toll is probably much higher. Airstrikes in the past week destroyed a theatre, a swimming pool complex, and an art school -- all sites where civilians were sheltering. In the besieged northern city of Chernihiv, Russian forces bombed and destroyed a bridge that was used for aid deliveries and civilian evacuations, regional governor Viacheslav Chaus said. Kateryna Mytkevich, who arrived in Poland after fleeing Chernihiv, wiped away tears as she spoke about what she had seen. The city is without gas, electricity or running water, said Mytkevich, 39, and entire neighborhoods have been destroyed. “I don’t understand why we have such a curse," she said. On Wednesday, the head of the International Committee of the Red Cross, or ICRC, traveled to Moscow for discussions with Russian officials on urgent matters including humanitarian aid and prisoners of war. “The devastation caused by the conflict in recent weeks, as well as eight years of conflict in Donbas, has been vast,” ICRC President Peter Maurer said. The war"s economic and geopolitical shockwaves — with soaring energy prices, fears for global food supplies, and Russia and China aligning in a new world order with Cold War echoes — have reverberated across a planet yet to emerge from the COVID-19 crisis. Key allies are meeting in Brussels and Warsaw this week to discuss possible new punitive measures and more military aid to Ukraine. As President Biden left the White House on Wednesday for the flight to Europe, he warned there is a “real threat" Russia could use chemical weapons and said he will discuss that danger with the other leaders. Meanwhile, talks between Kyiv and Moscow to end the fighting have continued by video. Zelenskyy said negotiations with Russia are going “step by step, but they are going forward”. With no peace, those not yet fighting prepared to do so. “Everything’s a best-seller these days," said Zakhar Sluzhalyy, who owns a gun shop in the western city of Lviv. "We’re defending our land,” he said. "We’re fighting for our freedom and that of the rest of Europe.” — Agencies