Fighting raged in Sievierodonetsk on Tuesday as Russian troops advanced toward the center of a city that has become a central focus for President Vladimir V. Putin’s forces since they failed to seize Ukraine’s capital, Kyiv, early in the war and pivoted to the east of the country.
Russian forces had occupied parts of Sievierodonetsk, an industrial city on the Seversky Donets River that is the last in the Luhansk region to remain outside Russian control, and were “gradually moving toward downtown,” the head of the Ukrainian military administration in Luhansk, Serhiy Haidai, said.
“Street fighting continues,” he said. Two civilians had been killed since Monday and four others were wounded.
Most of the city’s civilian prewar population of around 100,000 has fled in the face of a Russian artillery barrage that has endured for weeks, but 12,000 people, many of them elderly, are trapped in appalling conditions, according to an estimate by the Norwegian Refugee Council aid group.
Families and young people have largely left the city. Many of the older people who remain have health problems or disabilities that make flight impossible, according to Jan Egeland, secretary general of the Norwegian Refugee Council and a former United Nations humanitarian coordinator.
“It breaks my heart,” Mr. Egeland said in an interview. “It really is really a war on the elderly.” He called for a humanitarian cease-fire to allow for evacuations and the resupply of aid.
Ukrainian authorities halted attempts to evacuate civilians via a road leading to the city of Bakhmut on Monday after a French journalist was killed when the armored bus he was riding in was hit by shrapnel from what Ukrainian officials said was a Russian shell.
A relentless artillery barrage that has damaged as much as 90 percent of the city’s buildings has forced the residents who remain to hide in basements and bomb shelters, emerging briefly to cook food.
Mr. Egeland said he had visited his aid group’s operation in the city just before the war began and found it hard to believe how much had changed since. The group has now lost contact with the only staff member who remained there; in the last phone call with him, the staff member described the situation as horrendous, Mr. Egeland said.
Russian forces have pounded Sievierodonetsk for weeks with artillery. In recent days, they have seized two key points in the northeast of the city, a hotel and a bus station, and have also gained ground in the southeast.
Moscow has gained leverage in its effort to take the city by focusing its forces on the region, according to military analysts. In doing so, it may be starting to correct an error made at the outset of the invasion in February, when spreading its forces across the country contributed to Moscow’s failure to take Kyiv or the country’s second-largest city, Kharkiv.
Russian forces have fired on 46 settlements in the eastern provinces of Donetsk and Luhansk over the past day, killing at least three civilians and wounding seven others, Ukraine’s chief of staff said in a statement on Tuesday.