Unless new antibiotics are found, the rise of untreatable bacteria threatens a "unthinkable scenario" where once-treatable minor infections become fatal, he said.
As bacteria and viruses develop resistance to existing antibiotics, the effectiveness of such treatments naturally diminishes.
Cameron privately raised the issue with US President Barack Obama and German Chancellor Angela Merkel at the G7 summit last month and believes he has their agreement for a co-ordinated international push.
"This is not some distant threat but something happening right now," Cameron told The Times newspaper.
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"That simply cannot be allowed to happen and I want to see a stronger, more coherent global response."
Jim O'Neill, the former chief economist of US investment bank Goldman Sachs, is to lead an international expert group aiming to spark the development of a new generation of antibiotics.
He has been tasked with considering how developing countries can be encouraged to improve control of existing antibiotics, of which only five new types have been introduced since the 1960s.
"For many of us we only know a world where infections or sicknesses can be quickly remedied by a visit to the doctor and a course of antibiotics.
"But that protection is at risk as never before. Resistance to antibiotics is now a very real and worrying threat."
The initial USD 860,000 cost of the work will be met by the Wellcome Trust biomedical research charity.
Drug-resistant bacteria, viruses and parasites threaten not only the ability to treat deadly infections but also most aspects of modern medicine, said the trust's director Jeremy Farrar.
"We are failing to contain the rise of resistance, and failing to develop new drugs to replace those that no longer work. We are heading for a post-antibiotic age.