Writing in the New York Times, the prime minister said “it is not future historians but the people of Ukraine who will be our judge”.
Mr Johnson set out a six-point plan, including rapidly strengthening defences in Nato countries.
But Labour criticised the PM for not acting more quickly over sanctions.
Ahead of a series of meetings with international leaders, the prime minister said: “Putin must fail and must be seen to fail in this act of aggression.
“It is not enough to express our support for the rules-based international order – we must defend it against a sustained attempt to rewrite the rules by military force.”
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The invasion was condemned by 141 nations at the UN General Assembly while 39 countries, co-ordinated by the UK, made the largest-ever referral for war crimes to the International Criminal Court.
But Mr Johnson is set to call on world leaders to make a “renewed and concerted effort” to stop Russian President Vladimir Putin, Downing Street said.
In his six-point plan to maintain pressure on Mr Putin, the prime minister said:
- World leaders should mobilise an “international humanitarian coalition” for Ukraine
- They should also support Ukraine “in its efforts to provide for its own self-defence”
- Economic pressure on Russia should be ratcheted up
- The international community must resist Russia’s “creeping normalisation” of its actions in Ukraine
- Diplomatic resolutions to the war must be pursued, but only with the full participation of Ukraine’s legitimate government
- There should be a “rapid campaign to strengthen security and resilience” among Nato countries
The prime minister is also expected to deliver his message at meetings with Canadian Prime Minister Justin Trudeau and Dutch Prime Minister Mark Rutte at Downing Street on Monday.
On Tuesday, he will host leaders of the V4 group of central European nations: the Czech Republic, Hungary, Poland and Slovakia.
Downing Street says these countries are already experiencing a humanitarian crisis, with 1.4 million people fleeing Ukraine to neighbouring nations in just 10 days. Mr Johnson said: “The world is watching.”
The UK is also facing criticism it is not doing enough. Ukrainian nationals with family in the UK have said some of them are excluded from new visa programmes for refugees while Labour has called for emergency visas to be offered to any Ukrainian who can pass security checks.
Shadow foreign secretary David Lammy said the opposition fully supports the UK joining international efforts to provide “military, economic, diplomatic and humanitarian” support to Ukraine.
He said: “At home, the UK government must move faster and harder to impose sanctions on the oligarchs and politicians linked to the rogue Russian regime.
“It is inexcusable that we have fallen behind the EU and the US on the number of individuals and entities sanctioned. Ministers must move faster, acting against Putin’s cronies in days not months.”
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