Residents of the bombarded suburbs of Ukraine's capital snaked their way across the slippery wooden planks of a makeshift bridge that provided the only way to escape Russian shelling, amid renewed efforts on Wednesday to rescue civilians from besieged cities.

With sporadic gunfire echoing behind them, firefighters dragged an elderly man to safety in a wheelbarrow, a child gripped the hand of a helping soldier, and a woman inched her way along cradling a fluffy cat inside her winter coat. On the far side of the bridge, they all trudged past a crashed van with the words 'Our Ukraine' written in the dust coating its windows.

"We have a short window of time at the moment," said Yevhen Nyshchuk, a member of Ukraine's territorial defence forces. "Even if there is a cease-fire right now, there is a high risk of shells falling at any moment."

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 Ukraine. The UN estimates that more than two 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, Central Investigation Agency Director William Burns said on Tuesday.

In addition to the humanitarian crisis unfolding in many of Ukraine's cities, concerns for the safety of its nuclear plants amid fighting has raised alarm worldwide.

Read: Europe's largest nuclear power plant on fire after shelling

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

The diesel generators at Chernobyl, site of the world's worst nuclear accident in 1986, have fuel for 48 hours, power grid operator Ukrenerho said. The plant was shut down in 2000, but the deserted site still stores spent nuclear fuel from Chernobyl and other nuclear plants around Ukraine.

Authorities announced a new ceasefire on Wednesday to allow civilians to escape from towns around the capital, Kyiv, as well as the southern cities of Mariupol, Enerhodar and Volnovakha, Izyum in the east and Sumy in the northeast. Previous attempts to establish safe evacuation corridors have largely failed due to attacks by Russian forces.

It wasn't immediately clear how successful Wednesday's new effort was.

But some people did start streaming out of Kyiv's suburbs along an evacuation route that the Ukrainians said both sides had agreed to, even as explosions could be heard in the capital and air raid sirens sounded repeatedly. Many are headed for the city centre, from which they board trains bounded for western Ukrainian regions not under attack.

Meanwhile, a children's hospital in the Ukrainian city of Mariupol has been destroyed by Russian air strikes, the city council said in an online post.

“The Russian occupying forces have dropped several bombs on the children's hospital. The destruction is colossal,” it said, adding that it did not yet know any casualty figures.

Russia has, however, denied targeting civilians in its assault on Ukraine.

Read: Mariupol under siege, Russian aircraft pound Chernihiv

Russian advance continues

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

Still, Ukraine's general staff of the armed forces said the military is building up defences in cities in the north, south and east, and forces around Kyiv are holding the line against the Russian offensive.

That's even as the general staff said Russian forces are placing military equipment on farms and amid residential buildings in the northern city of Chernihiv.

In the south, Russians dressed in civilian clothes are advancing on the city of Mykolaiv, a Black Sea shipbuilding centre of a half-million people, it said.

Ukrainian resistance is stiffer than many expected and Western nations are rushing now to bolster their force.

Poland offers fighter planes for Ukraine's use

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.

Read: US says no to no-fly zones and troops for Ukraine

Poland late on Tuesday offered to give the US 28 MiG-29 fighter planes for Ukraine's use. US officials said that proposal was untenable, but they would continue to consult with Poland and other North Atlantic Treaty Organisation allies.

US to vote on Russian oil ban

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 US would ban all Russian oil imports, even if it meant rising costs for Americans.

The US House of Representatives was poised on Wednesday for a critical series of votes that would ban US imports of Russian oil, provide emergency aid to Ukraine and fund the federal government through September 30.

Lawmakers were expected to begin with a mid-morning vote to adopt the rules for a floor debate that would precede final votes on passage later in the day.

Democrats and Republicans reached a $1.5 trillion deal overnight to fund the federal government for fiscal year 2022, including $13.6 billion in security and humanitarian aid for Ukraine.

The House was also expected to vote on a bill to ban Russian energy imports. The legislation builds on President Joe Biden's newly announced ban by including moves to review Russia's membership in the World Trade Organisation. It would also renew and expand the Magnitsky human rights law to ease the way for further US sanctions on Russia.

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. McDonalds, 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.

"Economic war'

Meanwhile, the Kremlin accused the US of declaring an economic war on Russia that was sowing mayhem through energy markets, and put Washington on notice it was considering its response to a ban on Russian oil and energy.

Kremlin spokesman Dmitry Peskov cast the West's sanctions as a hostile act that had roiled global markets and he said it was unclear how far turbulence on global energy markets would go.

“You see the bacchanalia, the hostile bacchanalia, which the West has sown — and that of course makes the situation very difficult and forces us to think seriously,” Peskov told reporters.

“We see that the situation on energy markets is developing rather turbulently — and we don't know how far that turbulence will go,” Peskov said.

He declined to outline the exact nature of Russia's response.

Putin will hold a meeting with the government on Thursday to discuss minimising the impact of sanctions, the Kremlin said.

Russia says US has biolabs with plague and anthrax in Ukraine

Russia also said US must explain what Moscow claims was a military biological programme in Ukraine — an allegation Washington has already dismissed as "absurd" misinformation.

Russian foreign ministry spokeswoman Maria Zakharova said evidence of the alleged programme had been uncovered by Russia during what it calls its military operation in Ukraine, which its forces invaded on February 24. It involved deadly pathogens including plague and anthrax, she said.

A Ukrainian presidential spokesperson said: "Ukraine strictly denies any such allegation".

In response to earlier Russian allegations about the purported military biological programme in Ukraine, a Pentagon spokesman said on Tuesday: "This absurd Russian misinformation is patently false".

Zakharova said Russia had documents showing that the Ukrainian health ministry had ordered the destruction of samples of plague, cholera, anthrax and other pathogens after February 24.

Air raid alerts

A series of air raid alerts on 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.

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.

But in the south, Russian troops have advanced deep along Ukraines 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, which nearly half of the population of 430,000 is hoping to flee.

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 shouldnt 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. Im so sad about people and about the city, the children."