The Lugansk regional governor described the situation in Severodonetsk as "extremely complicated".
Russian forces have seized control of half of eastern Ukraine's key city of Severodonetsk, a senior official said Tuesday, hours after EU leaders struck a watered-down deal to ban more than two-thirds of Moscow's oil imports.
In central Ukraine, two Russian soldiers were sentenced to more than 11 years in jail each after a court found them guilty of firing artillery at civilian areas soon after Moscow's February 24 invasion.
Severodonetsk is one of several industrial hubs that lie on Russia's path to capturing the Donbas's Lugansk region, where Moscow has shifted the bulk of its firepower since failing to capture Kyiv in the war's early stages.
"Unfortunately, the front line divides the city in half. But the city is still defending itself, the city is still Ukrainian, our soldiers are defending it," said Oleksandr Stryuk, head of Severodonetsk's military and civil administration.
Lugansk regional governor Sergiy Gaiday earlier described the situation as "extremely complicated", conceding that parts of the city were controlled by Russian forces.
But as Russian troops edged closer to the Severodonetsk city centre, EU leaders at a summit in Brussels were tightening the economic screws on Moscow.
A compromise oil embargo deal reached late Monday, meant to punish Russia for its invasion, cuts "a huge source of financing for its war machine," European Council chief Charles Michel tweeted.
Hungarian Prime Minister Viktor Orban, one of the key figures who blocked an agreement by the 27-nation bloc, hailed the deal for preserving Budapest's supply of cheap crude from Moscow.
"Families can sleep peacefully tonight, we kept out the most hair-raising idea," Orban, whose country borders war-torn Ukraine to the west, said in a video message.
'Save your lives'
Ukrainian President Volodymyr Zelensky had urged Europe to forge their "independence" from Russian energy.
The situation on the eastern front line in Donbas has become increasingly desperate, with Ukrainian towns facing near constant shelling by Russian forces.
"We see some cars driving around with Ukrainian flags so we figure that means we are still part of Ukraine," said Yevgen Onyshchenko, a 42-year-old plumber in a powerless apartment in Severodonetsk's twin city Lysychansk.
"But otherwise, we are in the dark."
A French journalist, Frederic Leclerc-Imhoff, was killed while covering civilian evacuations in the area on Monday.
An overnight rocket attack killed at least three people and wounded six in the city of Slovyansk, Donetsk regional governor Pavlo Kirilenko said Tuesday on Telegram.
"I repeat once again that there are no safe places in the Donetsk region, so I call again: evacuate -- save your lives," he said.
In the southern region of Kherson, the country's military leadership said Ukrainian forces have pushed back, as prosecutors pressed ahead with prosecutions of captured Russian soldiers.
The servicemen convicted on Tuesday -- Alexander Bobykin and Alexander Ivanov -- were both handed sentences of 11 years and six months for firing Grad missiles on two villages in the north-eastern Kharkiv region in the early days of the war.
Gas 'quite different'
The verdict after the trial in the Poltava region comes one week after another court, in the capital Kyiv, gave a 21-year-old Russian solider a life sentence -- the country's first judicial reckoning on Russia's invasion.
Ukraine's prosecutor general was in The Hague on Tuesday meeting her counterpart from the International Criminal Court and other officials as they seek wider war crimes prosecutions.
But while Ukraine is pushing for solidarity from its allies, European leaders meeting on Tuesday for a second day played down the chances of a rapid embargo on Russian gas to follow the partial ban on oil imports.
Europe is heavily reliant on Russian gas.
"With gas it is quite different. Therefore the gas embargo will not be an issue in the next package of sanctions" Austrian Chancellor Karl Nehammer said.
The compromise oil deal hatched on Monday exempts deliveries by pipeline, after Orban warned halting supplies would wreck Hungary's economy.
EU chief Ursula von der Leyen said the ban "will effectively cut around 90 percent of oil imports from Russia to the EU by the end of the year".
The agreement also includes plans for the EU to send nine billion euros ($9.7 billion) in "immediate liquidity" to Kyiv, Michel announced.
'Sit in the trench'
Michel said the sanctions involved disconnecting Russia's biggest bank, Sberbank, from the global SWIFT system, banning three state broadcasters and blacklisting individuals blamed for war crimes.
Russia's Gazprom, meanwhile, turned off the tap to the Netherlands on Tuesday, halting gas shipments after Dutch energy firm GasTerra ignored a demand that gas supplied from April 1 be paid for in rubles.
Danish energy company Orsted has also warned its gas shipments could be cut off when a Tuesday payment deadline had passed.
Washington, however, is taking a cautious line regarding weaponry for Ukraine.
US President Joe Biden said Monday he would not send long-range rocket systems that could hit Russian territory, despite urgent requests from Kyiv for exactly that.
Ukraine has received extensive US military aid, with legislators approving another $40 billion assistance package in May.
But front-line Ukrainian soldiers getting pummelled by rocket and artillery fire said without long-range weapons to hit the Russians, it was not enough.
"If you know you have a heavy weapon behind you, everyone's spirits rise," one soldier who uses the nom de guerre Luzhniy told AFP.
"Otherwise, you just sit in the trench staring at the horizon."
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)