Boris Johnson is pledging to donate most of the UK's surplus vaccine supply to poorer countries in a speech to a virtual G7 meeting on Friday.
He urged rich countries to back a 100-day target for the developing new vaccines for future emerging diseases.
The UK has ordered more than 400 million doses of various vaccines, so many will be left over once all adults are vaccinated.
But anti-poverty campaigners say the UK is not doing enough.
Decisions on when and how much of the surplus will be distributed will be made later this year, with ministers taking into account the supply chain and whether booster shots are needed in the autumn.
The prime minister told his fellow leaders: "Science is finally getting the upper hand on Covid. Around the world [we need to] make sure everyone gets the vaccines that they need, so that the whole world can come through this pandemic together."
"There is no point in us vaccinating our individual populations - we've got to make sure the whole world is vaccinated because this is a global pandemic and it's no use one country being far ahead of another, we've got to move together."
He said he wanted to "ensure that we distribute vaccines at cost around the world - make sure everybody gets the vaccines that they need so that the whole world can come through this pandemic together."
After the meeting, the G7 leaders issued a statement committing to "intensify cooperation on the health response to Covid-19".
It reaffirmed the group's support for "affordable and equitable access to vaccines, therapeutics and diagnostics, reflecting the role of extensive immunisation as a global public good."
French President Emmanuel Macron has told the Financial Times richer countries should send up to 4 to 5% of their current vaccine supplies to poorer nations.
But Foreign Office minister James Cleverly told BBC Radio 4's Today programme the UK would be "looking at a figure significantly greater than that".
He promised the government would be a "global force for good" in fighting the pandemic and, unlike "some countries", the UK would not use the promise of vaccine supplies to other countries as "short-term diplomatic leverage".
But it was "difficult to say" at this stage when the sharing would happen, Mr Cleverly added.
A government source said more than half of excess doses would go to Covax, a UN initiative intended to ensure wider access to vaccines.
The UK government has donated £548m to the scheme, to which the US pledged $4bn (£2.9bn) in December.
Almost 17 million people in the UK have now received at least one vaccine dose, with 573,724 of these receiving two doses, according to the latest figures.
By Naomi Grimley, global health correspondent
In the global scramble to secure vaccines against Covid-19 many wealthy countries - which funded a lot of the research - have ended up buying more supplies than they need.
New figures from the anti-poverty pressure group, the One Campaign, reveal that Australia, Canada, Japan, the UK, and US and the EU have already secured more than 3bn doses - 1.2bn more than they need to give their entire populations two doses.
The UK has also given £548m to Covax - the UN-led attempt to get vaccines out to poorer countries.
But campaigners say they want hard facts on how many actual doses Britain will now be donating to the mechanism.
Some 130 countries in the world haven't done any vaccinations at all and healthcare workers in those countries remain at high risk.
And even if the Covax plan works, it's only designed to cover 20% of each nation's population - far short of the herd immunity expected in wealthy countries.
Mr Johnson used his position as chairman of the G7 group of major economies to push the case for setting a 100-day target for developing vaccines when new diseases strike.
He also told the group that it was important to "build back better" from the pandemic and face the "great challenges" of climate change, telling the leaders that he wanted "to get some great things done" at the G7 and the forthcoming Cop26 climate summit in Glasgow in November.
Friday's virtual meeting is the first gathering of G7 leaders since April 2020, and the first international meeting for new US President Joe Biden.
The One Campaign, which aims to end extreme poverty and preventable disease by 2030, said Mr Johnson's commitment to Covax did not go far enough.
UK director Romilly Greenhill said: "The virus won't wait on us to be ready before it mutates, so we need to get these vaccines around the world as quickly as possible."
An Ipsos MORI poll of people from 18 countries showed that those in the UK were most likely to support donating surplus doses.
Almost seven in 10 Britons (69%) want to pass on some of the country's extra doses to be used in other countries, whereas globally just under half (46%) say they would want their country to do this.
A further 12,057 new Covid cases were reported across the UK on Thursday, alongside another 454 deaths within 28 days of a positive test.
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