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Russian forces seized Lysychansk's sister city Sievierodonetsk on the opposite side of the Siverskiy Donets river last month, after some of the heaviest fighting of the war.
Rodion Miroshnik, ambassador to Russia of the pro-Moscow self-styled Luhansk People's Republic, told Russian television "Lysychansk has been brought under control," but added: "Unfortunately, it is not yet liberated."
Russian media showed video of Luhansk militia parading in Lysychansk streets waving flags and cheering, but Ukraine National Guard spokesman Ruslan Muzychuk told Ukrainian television the city remained in Ukrainian hands.
"Now there are fierce battles near Lysychansk, however, fortunately, the city is not surrounded and is under the control of the Ukrainian army," Muzychuk said.
Zelenskiy adviser Oleksiy Arestovych said Russian forces had finally crossed the Siverskiy Donets river and were approaching the city from the north.
"This is indeed a threat. We shall see. I do not rule out any one of a number of outcomes here. Things will become much more clear within a day or two.
"If Lysychansk is taken, strategically it becomes more difficult for the Russians to continue their offensive. The front lines will be flatter and there will be a frontal attack rather than from the flanks."
He said the Russians would have to focus on taking six major cities in the industrialised eastern Donbas region and with each their forces would be more and more thinly spread.
"The more Western weapons come to the front, the more the picture changes in favour of Ukraine," he said.
Ukraine has repeatedly appealed for more weapons from the West, saying its forces are heavily outgunned.
Elsewhere, Oleksandr Senkevych, mayor of Mykolaiv, which borders the vital Black Sea port of Odesa, reported powerful explosions in the city on Saturday.
"Stay in shelters!" he wrote on the Telegram messaging app as air raid sirens sounded.
The cause of the blasts was not immediately clear, although Russia later said it had hit army command posts.
Reuters could not independently verify the battlefield reports.
Ukrainian authorities said a missile slammed into an apartment block near Odesa on Friday, killing at least 21 people. A shopping mall was hit on Monday in the central city of Kremenchuk, killing at least 19.
Zelenskiy denounced the strikes on Friday as "conscious, deliberately targeted Russian terror and not some sort of error or a coincidental missile strike."
'VERY DIFFICULT PATH'
In his nightly television address on Saturday, Zelenskiy said it would be a "very difficult path" to victory but Ukrainians must maintain their resolve and inflict losses on the "aggressor ... so that every Russian remembers that Ukraine cannot be broken."
Kyiv says Moscow has intensified missile attacks on cities far from the main eastern battlefields and that it deliberately hit civilian sites. Ukrainian troops on the eastern front lines meanwhile describe intense artillery barrages on residential areas.
Thousands of civilians have been killed and cities levelled since Russia invaded Ukraine on Feb. 24. Kremlin spokesperson Dmitry Peskov repeated Russia's denials that it targets civilians.
Russia is seeking to drive Ukrainian forces out of Luhansk and Donetsk provinces in Donbas, where Moscow-backed separatists have been fighting Kyiv since Russia's first military intervention in Ukraine in 2014.
Troops on a break from the fighting and speaking in Konstyantynivka, a market town about 115 km (72 miles) west of Lysychansk, said they had managed to keep the supply road to the embattled city open, for now, despite Russian bombardment.
"We still use the road because we have to, but it's within artillery range of the Russians," said one soldier as comrades relaxed nearby, munching on sandwiches or eating ice cream.
"The Russian tactic right now is to just shell any building we could locate ourselves at. When they've destroyed it, they move on to the next one," he said.
Reuters reporters saw an unexploded missile lodged into the ground in a residential neighbourhood on the outskirts of the Donbas city of Kramatorsk on Saturday evening.
The missile fell in a wooded area between residential tower blocks. Outgoing artillery fire and several large explosions were heard in central Kramatorsk earlier in the evening.
Despite being battered in the east, Ukrainian forces have made some advances elsewhere, including forcing Russia to withdraw from Snake Island, a Black Sea outcrop southeast of Odesa that Moscow captured at the start of the war.
Russia had used Snake Island to impose a blockade on Ukraine, one of the world's biggest grain exporters and a major producer of seed for vegetable oils. The disruptions have helped fuel a surge in global grain and food prices.
Russia, also a big grain producer, blames the crisis on Western sanctions hurting its exports.