Renewed efforts to rescue civilians from increasingly dire conditions in besieged and bombarded Ukrainian cities were underway Wednesday. Days of shelling have largely cut residents of the southern city of Mariupol off from the outside world and forced them to scavenge for food and water.

Meanwhile, the decommissioned Chernobyl nuclear site was knocked off the power grid Wednesday and forced to switch onto generators. That raised alarm about the plant's ability to keep its nuclear fuel safely cool, though the U.N. nuclear watchdog said it saw “no critical impact on safety” from the power cut.

Authorities announced another cease-fire to allow civilians to escape from Mariupol, Sumy in the northeast, Enerhodar in the south, Volnovakha in the southeast, Izyum in the east, and several towns in the region around the capital, Kyiv.

Previous attempts to establish safe evacuation corridors have largely failed due to attacks by Russian forces, and there were few details on Wednesday's new effort. It was not clear if anyone was able to leave Mariupol, but some people did start streaming out of Kyiv's suburbs, even as air raid sirens repeatedly went off in the capital and explosions could be heard there.

Mariupol, which nearly half of the population of 430,000 is hoping to flee, has been surrounded by Russian forces for days. Corpses lie in the streets, and people break into stores in search of food and melt snow for water. Thousands huddle in basements, sheltering from the Russian shells pounding this strategic port on the Azov Sea.

“Why shouldn’t I cry?” resident Goma Janna demanded as she wept by the light of an oil lamp below ground, surrounded by women and children. “I want my home, I want my job. I’m so sad about people and about the city, the children.”

READ: Russia-Ukraine war: Chernobyl site knocked off power grid

Thousands of people are thought to have been killed, both civilians and soldiers, in two weeks of fighting since President Vladimir Putin’s forces invaded. The U.N. estimates that more than 2 million people have fled the country, the biggest exodus of refugees in Europe since the end of World War II.

The crisis is likely to get worse as Russian forces step up their bombardment of cities throughout the country in response to stronger than expected resistance from Ukrainian forces. Russian losses have been “far in excess” of what Putin and his generals expected, CIA Director William Burns said Tuesday.

An intensified push by Russian forces could mean “an ugly next few weeks,” Burns told a congressional committee, warning that Putin was likely to "grind down the Ukrainian military with no regard for civilian casualties.”

Britain’s Defense Ministry said Wednesday that fighting continues northwest of Kyiv. The cities of Kharkiv, Chernihiv, Sumy and Mariupol are being heavily shelled and remain encircled by Russian forces.

Adding to the dire humanitarian conditions were concerns about the safety of the Chernobyl plant, site of the world’s worst nuclear accident in 1986. Russian forces seized plant last week, and on Wednesday all its facilities were without power, the Ukrainian grid operator Ukrenerho said, citing the national nuclear regulator.

The diesel generators have fuel for 48 hours. Without power, the “parameters of nuclear and radiation safety” cannot be controlled, Ukrenerho said.

But the Vienna-based International Atomic Energy Agency later said that while the development violates a “key safety pillar on ensuring uninterrupted power supply,” it sees “no critical impact on safety.”

A reactor at Chernobyl exploded and caught fire in 1986. The plant was shut down in 2000, but the deserted site still stores spent nuclear fuel from Chernobyl and other nuclear plants around Ukraine. Experts have warned of catastrophic consequences if the war disrupts power to pumps that keep the radioactive fuel cool.

It was at least the third time that the Russian offensive raised the specter of a nuclear disaster.

Meanwhile, Russian forces are placing military equipment on farms and amid residential buildings in the northern city of Chernihiv, Ukraine’s general staff said. In the south, Russians dressed in civilian clothes are advancing on the city of Mykolaiv, a Black Sea shipbuilding center of a half-million people, it said.

The Ukrainian military, meanwhile, is building up defenses in cities in the north, south and east, and forces around Kyiv are “holding the line” against the Russian offensive.

That resistance is stiffer than many expected — and Western nations are rushing now to bolster their force. Ukraine's president has pleaded repeatedly for warplanes to counter Russia's significant air power, but Western countries have disagreed over how best to do that amid concerns it could raise the risk of the war expanding beyond Ukraine.

Poland late Tuesday offered to give the U.S. 28 MiG-29 fighter planes for Ukraine's use. U.S. officials said that proposal was “untenable,” but they would continue to consult with Poland and other NATO allies.

READ: Russia-Ukraine war: Shelling and evacuation efforts ongoing

In addition to material support for Ukraine, Western countries have sought to pressure Russia through a series of punishing sanctions. On Tuesday, President Joe Biden upped the ante further, saying said the U.S. would ban all Russian oil imports, even if it meant rising costs for Americans.

Energy exports have kept a steady stream of cash flowing to Russia despite otherwise severe restrictions that have largely cut its economy off from the world. McDonald’s, Starbucks, Coca-Cola, PepsiCo and General Electric all announced that they’re temporarily suspending business in the country, furthering that isolation.

The moves have done little to blunt the conflict so far.

A series of air raid alerts Wednesday morning urged residents of the capital to go to bomb shelters amid fears of incoming missiles. Associated Press reporters later heard explosions.

Such alerts are common, though irregular, keeping people on edge. Kyiv has been relatively quiet in recent days, though Russian artillery has pounded the outskirts of the city.

On those outskirts, police officers and soldiers helped elderly residents from their homes on Tuesday. People crowded together under a destroyed bridge before crossing a river on slippery wooden boards as they tried to escape Irpin, a town of 60,000 that has been targeted by Russian shelling.

Kyiv regional administration head Oleksiy Kuleba said the crisis for civilians was growing in the capital, with the situation particularly critical in the city’s suburbs.

“Russia is artificially creating a humanitarian crisis in the Kyiv region, frustrating the evacuation of people and continuing shelling and bombing small communities,” he said.

Amid the bombardments, authorities have tried repeatedly to evacuate civilians, but many attempts have been thwarted by Russian shelling.

One evacuation did appear successful on Tuesday, with Ukrainian authorities saying 5,000 civilians, including 1,700 foreign students, had managed to escape from Sumy, an embattled northeastern city of a quarter-million people.

That corridor was to reopen for 12 hours on Wednesday, with the buses that took people southwest to the city of Poltava the day before returning to pick up more refugees, regional administration chief Dmytro Zhyvytskyy said.

Priority was being given to pregnant women, women with children, the elderly and the disabled.

In the south, Russian troops have advanced deep along Ukraine’s coastline in an effort to establish a land bridge to Crimea, which Moscow seized from Ukraine in 2014.

That has left Mariupol encircled by Russian forces.

On Tuesday, an attempt to evacuate civilians and deliver badly needed food, water and medicine failed, with Ukrainian officials saying Russian forces fired on the convoy before it reached the city.

Natalia Mudrenko, a senior member of Ukraine’s UN Mission, told the Security Council that the people of Mariupol have “been effectively taken hostage” by the siege. Her voice shook with emotion as she described how a 6-year-old died shortly after her mother was killed by Russian shelling. “She was alone in the last moments of her life,” she said.

Theft has become widespread in the city as beleaguered residents search for food, clothes, even furniture. Some residents are reduced to scooping water from streams. Authorities say they plan to start digging mass graves for the dead.

With the electricity out, many people rely on their car radios for information, picking up news from stations broadcast from areas controlled by Russian forces or Russian-backed separatists.

Ludmila Amelkina, who was walking along an alley strewn with rubble and walls pocked by gunfire, said the destruction had been devastating.

“We don’t have electricity, we don’t have anything to eat, we don’t have medicine. We’ve got nothing,” she said, looking skyward.