He said the "priority is a clear plan to vaccinate the world".
He went on: "The delta variant shows no-one is safe from this virus until everybody is.
"The PM has made big promises on this but it needs a truly global effort to make it happen, so will the PM take the lead at G7 and do whatever is necessary to make global vaccinations a reality?"
In response, Mr Johnson praised the vaccine effort and the government's role in the Oxford/AstraZeneca vaccine which, he said, made up a third of doses distributed globally.
He said: "That is global Britain in action to say nothing of the billion vaccines we hope to raise from the G7 next week."
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The calls from Labour come amid criticism, including from Conservative backbenchers, about the government's to cut foreign aid to 0.5% of national income from 0.7%.
Sir Keir Starmer said Mr Johnson's comments about the UK's role in the vaccine effort "would sound a lot better if the prime minister wasn't the only G7 leader cutting his aid budget".
SNP leader Ian Blackford also criticised the prime minister for the cuts saying they were "inhumane".
He called on Mr Johnson to commit to a vote on the issue, as Speaker Sir Lindsay Hoyle encouraged on Monday, and accused the government of "walking away from millions still struggling from the Covid pandemic and a poverty pandemic".
In response, Mr Johnson called criticism of the cut "lefty propaganda" and said "the people of this country... were given a vote on this and many other matters very recently I think they adjudicated very firmly in favour of the balance the Government is striking".
Mr Blackford replied that he had never heard former prime minister Theresa May, who spoke out against the cut on Tuesday, "called a leftist propagandist".
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