The US and Britain have announced bans on Russian oil, a significant move in piling pressure on President Vladimir Putin to halt his forces’ devastating assault on Ukraine.

The civilian death toll in the conflict mounted by Wednesday morning, with the number of refugees who have fled Ukraine to neighbouring countries surging past two million.

The United Nations human rights office said it had verified 1335 civilian casualties in Ukraine, including 474 killed and 861 injured.

There were allegations of hundreds of civilian casualties in Volnovakha, Mariupol and other urban areas from bombing and shelling of residential areas, it said.

Ukraine’s government accused Russian forces of shelling a humanitarian corridor that Russia had promised to open to let residents flee the besieged port of Mariupol.

US President Joe Biden said he must hold Russia “accountable for its unprovoked and unjustified attack on Ukraine”.

“Russia may continue to grind out its advance at a horrible price but this much is already clear: Ukraine will never be a victory for Putin,” Mr Biden said at the White House early on Wednesday.

“Putin may be able to take a city but he’ll never be able to hold the country.”

As Russia is a major producer of oil and natural gas, Western countries had been avoiding imposing sanctions on its energy sector in order to prevent widespread price hikes.

Mr Biden, who was under pressure from the US Congress to do more against Russia, warned Americans to prepare to pay more at the bowser.

• Read more: Shell to stop buying Russian oil and gas

Announcing the US ban on Russian energy imports, Mr Biden said: “That means Russian oil will no longer be acceptable in US ports and the American people will deal another powerful blow to Putin’s war machine.”

The US is not a leading buyer of Russian oil but Mr Biden has worked with allies in Europe, who are far more reliant on it, to isolate Russia’s energy-heavy economy and Mr Putin.

The EU has also published plans to cut its reliance on Russian gas by two thirds this year.

• Related: Anger at big companies still operating in Russia

Meanwhile, British Prime Minister Boris Johnson announced the UK would stop importing Russian oil, a move that his business minister said would be implemented gradually by the end of the year to minimise supply disruptions.

Ukraine calls for more help against ‘terrorist state’

That came amid emotional scenes in the British parliament where Ukrainian President Volodymyr Zelensky urged the world to increase the sanctions.

Speaking via videolink, Mr Zelensky said his people would fight to the end against the Russian invaders but it needed help – including no-fly zones.

“The question for us now is to be or not to be,” said Mr Zelensky, quoting Shakespeare.

“I can give you a definitive answer: it’s definitely to be.”

He continued: “We will not give up and we will not lose. We will fight to the end at the sea, in the air, we will continue fighting for our land, whatever the cost. We will fight in the forests, in the fields, on the shores, in the streets.”

Mr Zelensky urged world leaders to consider Russia a “terrorist state”.

“Please increase the pressure of sanctions…and please make sure that our Ukrainian skies are safe,” he said.

Lawmakers gave the speech a standing ovation.

Mr Johnson said Britain would “press on” with supplying Ukraine with weapons and to “tighten the economic vice” around Mr Putin.

“We will employ every method that we can: diplomatic, humanitarian and economic…until Vladimir Putin has failed in this disastrous venture, and Ukraine is free once more,” he said to cheers from MPs.

Sanctions imposed over the invasion have already cut off Russia from international trade and financial markets.

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Civilians trapped

In Mariupol, hundreds of thousands of people have been sheltering under bombardment without water or power for more than a week.

Many tried to leave on Tuesday along a safe corridor but Ukraine said they came under Russian fire.

“Ceasefire violated! Russian forces are now shelling the humanitarian corridor from Zaporizhzhia to Mariupol,” Ukraine’s foreign ministry spokesperson Oleg Nikolenko wrote on Twitter.

Mr Zelensky said a child had died of dehydration in Mariupol because water was cut off.

This could not be independently verified.

Russia opened a separate corridor allowing residents out of the eastern city of Sumy on Tuesday, the first successful evacuation under such a safe route.

Buses left Sumy for Poltava further west, only hours after a Russian air strike which regional officials said had hit a residential area and killed 21 people.

Reuters could not verify the incident.

Russia said 723 people had left the region via the Sumy-Poltava corridor, including 576 Indian citizens, in a first convoy.

Residents were also leaving Irpin, a frontline Kyiv suburb.

Ukraine says a Russian Kalibr missile was shot down over Kalynivka village, near Brovary, the eastern frontline of Kyiv. Photo: AAP

Russia denies targeting civilians and describes its actions as a “special operation” to disarm Ukraine and unseat leaders it calls neo-Nazis.

Ukraine and its allies call this a baseless pretext to invade a country of 44 million people.

The corridors to let civilians escape and allow aid reach besieged areas have been the main subject of talks between Russian and Ukrainian delegations.

The Interfax news agency said Russia was opening humanitarian corridors for the cities of Sumy, Mariupol, Chernihiv, Kharkiv and the capital Kyiv.

Ukraine has rejected Russian proposals for Kharkiv and Kyiv that would lead evacuees to Russia or its ally Belarus.

Earlier attempts at the weekend to allow residents to leave Mariupol failed, with each side accusing the other of continuing to fire.

-with AAP