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Foreign Secretary Liz Truss has said she supports individuals from the UK who might want to go to Ukraine to join an international force to fight.
She told the BBC it was up to people to make their own decisions, but argued it was a battle "for democracy".
She said Ukrainians were fighting for freedom, "not just for Ukraine but for the whole of Europe".
Ukraine's President Volodymyr Zelensky has urged foreign nationals "to join the defence of security in Europe".
Earlier on Sunday, he said Ukraine was setting up an "international" legion of volunteers for foreigners wishing to join the Ukrainian army in its fight against Russian forces.
"This is not just Russia's invasion of Ukraine, this is the beginning of a war against Europe. Against European unity," Mr Zelensky was quoted as saying on his official website.
"Everyone who wants to join the defence of security in Europe and the world may come and stand shoulder to shoulder with Ukrainians against the invaders of the 21st Century."
The UK government has stressed that British troops will not be sent to fight on the ground. Defence Secretary Ben Wallace said Ukraine would instead be supported to "fight every street with every piece of equipment we can get to them"
Ukrainian forces are currently battling Russian troops on the streets of Ukraine's second city Kharkiv, according to local officials.
Regional governor Oleh Sinegubov said light vehicles had entered the city, as he urged its 1.4 million residents to stay indoors.
Russia attacks Ukraine: More coverage
Ukraine's ambassador to the UK Vadym Prystaiko said an "overwhelming" number of foreign nationals were "demanding to be allowed to fight" for Ukraine - as the Russian invasion reaches its fourth day. Ukraine has said it will arm all volunteers.
Asked on BBC One's Sunday Morning programme, if she would support people from Britain going over to Ukraine to help in the fight , Ms Truss said: "I do support that, and of course that is something that people can make their own decisions about.
"The people of Ukraine are fighting for freedom and democracy not just for Ukraine, but for whole of Europe because that's what President Putin is challenging."
She said the UK government was "doing all it can" to support Ukraine with defensive weapons on the ground and with "far more severe sanctions" against Russia, to stop Putin from funding his "war machine".
"We are seeing a huge united effort, across the G7, across our allies, to challenge Vladimir Putin," she said. "Because this is Putin's war. This is pre-fabricated, pre-ordained aggression to try and subvert a sovereign democracy.
"We simply cannot allow him to succeed."
The foreign secretary said she feared the invasion of Ukraine would be a "bloody and long-running conflict" - with consequences felt far beyond Ukraine itself.
She said the UK "will need to do more [and] spend more" - citing the unprecedented sanctions announced by the government earlier this week, and Saturday's decision by the EU, US and their allies to cut off a number of Russian banks from the main international payment system, Swift.
"The aim is to degrade the Russian economy - to stop the money Putin has used to fund his war machine," she said.