Up to 100,000 people have fled the Ukraine capital of Kyiv as Russian tanks rolled onwards towards the city.
Around 137 people have so far been killed in the invasion.
However, that is expected to increase considerably as Russia increases its attack on its neighbour.
Ukrainian president Volodymyr Zelenskiy last night vowed to stay in Kyiv.
He also appealed to men in the country aged between 18 and 60 to stay and fight against the Russian army.
US secretary of state Antony Blinken warned that “all evidence suggests that Russia intends to encircle and threaten” the city.
“We believe Moscow has developed plans to inflict widespread human rights abuses – and potentially worse – on the Ukrainian people,” Mr Blinken said.
Mr Zelenskiy said “My family is the number two target. They want to destroy Ukraine politically by destroying the head of state. I will stay in the capital. My family is also in Ukraine.”
The Ukrainian president also voiced frustration after speaking to the heads of Nato member states.
“We have been left alone to defend our state,” Zelenskiy said. “Who is ready to fight alongside us? I don’t see anyone. Who is ready to give Ukraine a guarantee of Nato membership? Everyone is afraid.”
The British defence secretary Ben Wallace has said that Russia intends to take the whole of Ukraine but the Russian army failed to deliver on the first day of its invasion.
