US President Joe Biden has signed a memorandum to provide up to 600 million dollars (£448 million) in “immediate military assistance” to Ukraine as Kyiv officials warned street fighting was under way against Russian forces in the city.

Ukraine’s president refused a US offer to evacuate him from Kyiv hours after the UK, US and the European Union announced plans to impose personal sanctions on President Vladimir Putin and his foreign minister Sergei Lavrov in response to the Kremlin assault on Ukraine.

Mr Biden’s later memorandum directed secretary of state Antony Blinken to provide, subject to the Foreign Assistance Act of 1961, “immediate military assistance to Ukraine” of up to 250 million dollars (£187 million) “in assistance without regard to any provision of law”. Another 350 million dollars (£261 million) was allocated “in defence articles and services of the Department of Defence, and military education and training”.

It came as authorities in Kyiv urged residents to seek or remain in shelters, avoid going near windows or on balconies and take precautions against being hit by debris or bullets.

Ukrainian President Volodymyr Zelensky turned down a US offer to evacuate him from the city, with a US official quoting him as saying in response: “The fight is here; I need ammunition, not a ride.”

Hours later, Mr Zelensky shared a video of himself in central Kyiv and encouraged people to “not believe fake news. I am here”.

As Ukrainians continued to flee across their borders, Boris Johnson said he would be bringing forward measures “imminently”, while the White House and Brussels said they will freeze the assets of Mr Putin and Mr Lavrov.

Britain said that it was also extending a ban of Aeroflot flights landing in the UK to cover Russian private jets favoured by Moscow’s oligarchs.

At a meeting of the United Nations Security Council in New York, Russia – as expected – used its veto to block a motion calling for Moscow to cease the attack and withdraw its troops.

The UK’s ambassador to the UN, Dame Barbara Woodward, called the veto “absurd” and said Russia was “isolated”, adding: “History will record how we voted today and which countries stood up to be counted in defence of the charter and the sovereignty and territorial integrity of Ukraine.”

There was disappointment in Western capitals that India and the United Arab Emirates joined China in abstaining, weakening the international show of opposition to Russia’s actions.

Foreign Secretary Liz Truss noted Russia’s isolation and called Moscow “a global pariah”.

“Putin’s invasion of Ukraine and violation of the UN Charter will have severe consequences,” Ms Truss added.

Despite escalating economic measures, there was no sign they were having any impact on Mr Putin’s determination to pursue his military offensive against his neighbour which began on Thursday.

Western officials expressed concern that Russia could deploy devastating thermobaric weapons, amid signs that the advance of troops had been slower than planned in the face of stiff Ukrainian resistance.

The so-called “vacuum bombs” suck in oxygen to create powerful, high-temperature explosions which can damage internal organs.

“My fear would be that if they don’t meet their timescale and objectives, they would be indiscriminate in their use of violence,” one official said.

The latest intelligence update from the Ministry of Defence in London said Russian forces made advances throughout Friday – with a probable amphibious landing in southern Ukraine around Mariupol.

However the primary target remains Kyiv, with Russian forces advancing on “multiple axis” in an attempt to encircle the city.

With reports of sporadic fighting in the suburbs, there are fears of heavy civilian casualties as the main body of Russian troops reaches the capital.

Britain’s Chief of Defence Intelligence, Lieutenant General Sir Jim Hockenhull, said Moscow’s objective was to “secure control of the population and change the regime”.

After Mr Putin appealed to Ukrainian troops to rise up against their leaders and cease fighting, Mr Johnson issued his own appeal to the Russian people.

In a video posted on social media, he warned their country faced “complete isolation” as a result of their leader’s “needless and bloody war” which would mean many Russian soldiers “will never see their families again”.

Speaking briefly in Russian, he said: “I do not believe this war is in your name.”

Nato leaders agreed on Friday to send elements from the alliance’s 40,000-strong response force to protect member states in the east amid fears they could be the next target of Russian aggression.

Nato secretary general Jens Stoltenberg said it was clear the Kremlin’s objectives were “not limited to Ukraine” and that the alliance would “do what it takes to protect and defend every ally and every inch of Nato territory”.

“We are facing a new normal in European security where Russia openly contests the European security order and uses force to pursue its objectives,” he said.

Meanwhile, Facebook said it was “prohibiting Russian state media from running ads or monetising on our platform anywhere in the world”.