The possibility had been discussed “ages ago”, the UK prime minister said. But, he added: “Volodymyr has always been clear, his duty is to the Ukrainian people; he’s going to stay there, he’s going to look after them.”
“I have to say I admire him,” Mr Johnson added.
He also praised Mr Zelensky as a “heroic war leader” for the way he has “brought his people together” and “mobilised the world.”
At the beginning of the war last month, United States president Joe Biden had also offered to evacuate Mr Zelensky from Kyiv, but he had rebuked him by saying: “I need ammunition, not a ride!”
The Ukrainian president has periodically released visuals addressing his citizens to assure them that he is not leaving his country.
Meanwhile, Mr Johnson told the Sunday Times in an interview that the Ukrainian president has regular conversations with him and that he is an “absolutely charming guy but he’s also proved to be an inspiration”.
“I have a very, very strong desire to support him in any way I can,” he said, while not ruling out the possibility of visiting the Ukrainian. “Whether that would be a useful way of showing my support I don’t know but it is of huge, strategic, political, economic, moral importance for Putin to fail and Zelensky to succeed.”
Mr Johnson said that he hopes Kyiv “never falls”.
More than 150,000 people in the UK have offered to give homes to refugees under the government’s new sponsorship scheme. Mr Johnson said: “What the British public are doing I think is incredible. It is amazing and I think that it will be a great experience and that both the families that take them in and the evacuees themselves will benefit.”
On 24 February, Russian president Vladimir Putin launched a “special military operation” in Ukraine to “de-militarise” and “de-Nazify” the country.
More than three weeks into the invasion, the Russian advance on Ukraine’s major cities appears to have stalled.
The Kremlin’s forces are instead concentrating efforts on artillery and missiles strikes, with analysts and western intelligence saying that Mr Putin has turned to a war of attrition that could result in many more civilian casualties.
Meanwhile, the UN has confirmed at least 902 civilian deaths in the war, and said that more than 10 million people had now been displaced across Ukraine.
In the latest from Ukraine, at least eight people were reported to have died after Russia carried out a missile attack on a central Kyiv district, destroying a shopping centre overnight.
The Independent has a proud history of campaigning for the rights of the most vulnerable, and we first ran our Refugees Welcome campaign during the war in Syria in 2015. Now, as we renew our campaign and launch this petition in the wake of the unfolding Ukrainian crisis, we are calling on the government to go further and faster to ensure help is delivered.
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