As Russian forces battle for control of a key eastern Ukrainian city, up to 12,000 civilians may be trapped in the crossfire, according to the Norwegian Refugee Council (NRC).

"I am horrified to see Severodonetsk, the thriving city where we had our operational headquarters, become the epicentre of yet another chapter of the brutal war in Ukraine," NRC Secretary-General Jan Egeland said in a statement Tuesday. "We fear that up to 12,000 civilians remain caught in crossfire in the city, without sufficient access to water, food, medicine or electricity. The near-constant bombardment is forcing civilians to seek refuge in bomb shelters and basements, with only few precious opportunities for those trying to escape."

Over the past week, the Oslo-based humanitarian organization has been working with local Ukrainian partners to provide thousands of monthly food and hygiene parcels to civilians remaining in Severodonetsk and the greater Luhansk Oblast, according to Egeland. The city is the last still held by Ukrainian forces in Luhansk Oblast.

"But now the intensified fighting makes aid delivery impossible," he added. "We cannot save lives under the hail of grenades."

NRC has been operational in Ukraine since 2014, serving people affected by conflict in the Luhansk and Donetsk oblasts of eastern Ukraine's war-torn Donbas region.

"Almost one hundred days since the war in Ukraine escalated, we have seen bombs destroy critical infrastructure across the country and reduce entire cities like Severodonetsk to rubble," Egeland said. "More than 14 million men, women and children are displaced within Ukraine or sheltering in other countries with no idea when they will be able to safely return to their homes."

Russian and Ukrainian forces are believed to be fighting street by street on the outskirts of Severodonetsk, a key city in Ukraine's east, the U.K. Ministry of Defense said Tuesday in an intelligence update.

"Russia's capture of Lyman supports its operational main effort, which likely remains the encirclement of Sieverodonetsk and the closure of the pocket around Ukrainian forces in Luhansk Oblast," the ministry said. "Heavy shelling continues, while street fighting is likely taking place on the outskirts of Sieverodonetsk town."

After several days of fighting, the Russian military claimed Saturday to have fully seized the strategic town of Lyman, which serves as a railway hub in the Donetsk Oblast, west of Severodonetsk.

"Russia's political goal is likely to occupy the full territory of Donetsk and Luhansk Oblasts," the ministry added. "To achieve this, Russia will need to secure further challenging operational objectives beyond Sieverodonetsk, including the key city of Kramatorsk and the M04 Dnipro-Donetsk main road."

The European Union has agreed to partially ban Russian oil exports to the EU, leaders announced on Monday.

The new ban "immediately" covers more than two-thirds of oil imports from Russia, "cutting a huge source of financing for its war machine," Charles Michel, president of the European Council, tweeted on Monday.

"We agreed in Versailles to phase out our dependency on Russian gas, oil & coal as soon as possible," European Commission President Ursula von Der Leyen tweeted. "But this requires a plan."

-ABC News' Christine Theodorou

Bridget Brink, the new U.S. ambassador to Ukraine, has arrived in Kyiv, the U.S. Embassy confirmed.

Brink was nominated by President Joe Biden in April and confirmed by the Senate on May 18.

-ABC News' Christine Theodorou

Jalina Porter, the State Department's deputy spokesperson, is responding to the Russian attack at a Ukraine train station that killed at least 50, saying, "We can no longer be surprised by the Kremlin's repugnant disregard for human life."

Five children were among those killed when Russian rockets struck the station in Kramatorsk in Donetsk Oblast on Friday morning, according to Ukraine's state-owned railway company. At least 100 people were injured, according to Donetsk Oblast Gov. Pavlo Kyrylenko.

Russia has denied involvement in the attack, which occurred as "thousands" of civilians fleeing the Russian invasion were at the train station waiting to be taken to "safer regions of Ukraine," according to Kyrylenko.

"Civilians are killed when they stay in their homes, and they're killed when they try to leave," Porter said. "Actions like these demonstrate why Russia did not belong on the U.N. Human Rights Council, and they also reinforce the U.S. assessment that members of Russian forces are committing war crimes in Ukraine."

Porter declined to say if the department considers the train station attack a war crime, saying, "Assessing individual criminal liability in specific cases is the responsibility of courts, as well as other investigatory bodies. But as the secretary, Secretary [of State Antony] Blinken, has said, 'Those responsible for war crimes and other atrocities committed in Ukraine will be held to account.'"

-ABC News' Conor Finnegan