The G7 is formed of the UK, the US, Canada, France, Germany, Italy and Japan.
Mr Miliband said that the group should rally around their shared democratic values amid global vaccine diplomacy.
“We say the Group of Seven,” he said, “it’s the group of seven leading industrialised democratic countries.”
He added it was important that the UK maximise the potential of its vaccine programme on the world stage as a counterweight to the power of autocratic countries.
He said: “Because I promise you, the Chinas of this world, the Russias of this world, they’re thinking about vaccine diplomacy in geopolitical terms.
“They’re laying down a challenge.
“Their challenge is ‘autocracy works better than democracy.’
He said: “Our nation is going to be the arsenal of vaccines for the rest of the world.”
Meanwhile, China has accelerated its vaccines program after a slow start, injecting more people in 10 days in May than it had in the first three months of 2021.
The WHO recently gave emergency authorisation for two Chinese vaccines, and China has been proactive in sharing vaccines abroad, largely to African countries.
China has said its vaccines and its foreign investments come without political obligations, but has been expanding its global reach and influence in recent years.