Russia's separatist proxies in eastern Ukraine claimed full control of the important battlefield town of Lyman on Friday, and Ukraine appeared to concede it, as Moscow presses its biggest advance for weeks. Lyman, site of a key railway hub, has been a major front line as Russian forces press down from the north, one of three directions from which they have been attacking Ukraine's industrial Donbas region. The pro-Russian Donetsk People's Republic separatists said they were now in full control of it. Oleksiy Arestovych, adviser to Ukrainian President Volodymyr Zelenskiy, appeared to confirm the fall of Lyman in an interview overnight, and said the battle there showed that Moscow was improving its tactics. "According to unverified data, we lost the town of Lyman. The Russian army - this must be verified - captured it," Arestovych said in a video posted on social media. "Moreover, the way they captured it.... correctly organising the operation. This shows, in principle, the increased level of operational management and tactical skills of the Russian army. It has grown. It has not grown everywhere of course, but it has unquestionably grown." After being driven back from the capital Kyiv in March and from the outskirts of the second biggest city Kharkiv earlier this month, Russian forces are staging their strongest advance in weeks in the eastern Donbas region. Western military analysts say the battle there could prove decisive, depending on whether Russian forces can sustain the advance or run out of momentum. Further east, Russian forces have been trying to encircle Ukrainian troops in the cities of Sievierodonetsk and Lyshchansk, after breaking through Ukrainian lines further south in the city of Popasna last week. Popasna, reached by Reuters journalists in Russian-held territory on Thursday, was a blasted wasteland of burnt-out highrise apartments and shattered municipal buildings. Russian tanks and other military vehicles tore through the rubble-strewn streets kicking up dust with their treads, and low-flying attack helicopters thundered overhead. The bloated body of a dead man in uniform lay in a courtyard. Natalia Kovalenko, a resident, had finally come up in recent days from the cellar where she had been sheltering, to sleep amid the wreckage of her own flat. The balcony had been blown away and windows blasted off by a direct hit from a shell. She stared out wistfully into the blasted courtyard, recounting how two people had been killed there and eight wounded by a shell when they went outside to cook. Inside her flat, her kitchen and living room were filled with rubble and debris, but she had tidied a small bedroom to sleep. She was tired of being trapped in the cellar with dogs and cats. "I just have to fix the window somehow. The wind is still bad. Cold at night," she said. "We are tired of being so scared. So tired." 'WHAT PRICE' In an overnight address, Zelenskiy criticised the European Union for taking too long to ban Russian energy imports, saying the bloc was sending Moscow a billion euros a day which was funding the Kremlin's war effort. He said some countries were blocking efforts to agree new sanctions, an apparent reference to Hungary, which has objected to an EU ban on Russian oil. "Pressure on Russia is literally a matter of saving lives. Every day of procrastination, weakness, various disputes or proposals to 'pacify' the aggressor at the expense of the victim merely means more Ukrainians being killed," he said. Western countries led by the United States have provided Ukraine with long-range weaponry, including M777 howitzers and Harpoon anti-ship missiles from Denmark. Ukraine says it wants longer range ground weapons, especially rocket launchers, that can help it win an artillery battle against Russian forces in the east. It now looks likely to get them. U.S. officials say the Biden administration is even considering supplying Kyiv with the M142 High Mobility Artillery Rocket System (HIMARS), which can have a range of hundreds of kilometers. One concern that had held Washington back from supplying longer range arms in the past is the danger of escalation should Ukraine use them to hit targets deep within Russia. U.S. and diplomatic officials told Reuters Washington has held discussions with Kyiv about the issue. "We have concerns about escalation and yet still do not want to put geographic limits or tie their hands too much with the stuff we're giving them," said one U.S. official, speaking on condition of anonymity. A second U.S. official, also speaking on condition of anonymity, said Washington and Kyiv had a shared "understanding" about the use of certain Western-provided weapons: "So far, we've been on the same page about the thresholds." Russian Foreign Minister Sergei Lavrov warned that any supplies of weapons that could reach Russian territory would be a "a serious step towards unacceptable escalation". Russia calls its invasion of Ukraine a "special military operation" to defeat "Nazis" there. The West describes this as a baseless justification for a war of aggression.