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The latest financial commitment brings the total UK humanitarian aid package for the country to £120m.
The money is being provided to save lives and protect vulnerable people in Ukraine and the wider region, and to tackle the growing humanitarian crisis, the Foreign, Commonwealth and Development Office said.
About £40m was announced last weekend to help aid agencies respond to the deteriorating situation in Ukraine, giving access to basic necessities and medical supplies.
A £100m economic package of official development assistance funding for Ukraine was announced this month to bolster the economy and reduce its reliance on Russian gas imports.
Mr Johnson and Foreign Secretary Liz Truss said there was a duty to help.
“With every hour, the passionate desire of the people of Ukraine to defend their country has become more apparent and millions of people around the world have been stirred and moved by their courage," Mr Johnson said.
“The reality is that whatever happens in the coming days or weeks, the Ukrainian people have shown already that their spirit will not be broken and they will not be subdued.
“We as the international community have a responsibility to do everything we can to help the Ukrainians.”
Ms Truss said: “We have a moral duty to support Ukrainians affected by Putin’s unprovoked aggression.
"Britain is at the forefront of efforts to supply life-saving humanitarian aid, as well as political, economic and defensive support.
“Our message to the Ukrainian people is simple: we will help you and stand with you in the fight for the freedom and sovereignty of Ukraine.”
Mr Johnson, who on Tuesday was visiting Nato members Poland and Estonia to shore up support for the defence alliance, has ruled out British forces fighting in Ukraine.
He said Nato allies were not considering approval of Ukraine’s appeal to enforce a no-fly zone over the nation to prevent bombing by Russian planes.