Mr Cameron was addressing scientists, politicians and campaigners from around the world who have gathered in London for a dementia summit called by the UK as part of its year-long chairmanship of the G8.
With the World Health Organisation forecasting that numbers of dementia sufferers will almost double worldwide every two decades, Mr Cameron has said he wants UK Government investment in dementia research to double from £66 million in 2015 to £122m in 2025 - with similar increases from the commercial and charitable sectors.
Current estimates suggest 35.6million people around the world are living with dementia, including about 800,000 in the UK. Experts say there are likely to be nearly a million with the condition in the UK by the end of 2020.
Dementia is incurable and ultimately leaves people needing full-time care as brain function wastes away.
The London conference is expected to agree to a package of measures on international information-sharing and collaboration in research.
Mr Cameron said he hoped it would mark the point when "the global fightback really started, not just in finding a cure for dementia, but also in preventing it, delaying it and, crucially, helping those with dementia to live well and with dignity." He said he wanted the UK's life sciences industries to play "a leading role" in the fight against dementia.
The Prime Minister announced three new investments in life sciences, including £200m from GlaxoSmithKline, £150m from the Medical Research Council for clinical infrastructure for dementia and genomics and £3m from Belgian pharmaceutical company UCB for its research centre in Slough.
He told the conference the world should be "just as resolute" in tackling dementia as it had been in the past in seeking treatments and cures for killer diseases such as malaria, cancer and HIV/Aids.
"The challenge is huge and we are a long way from a cure, but there is hope," he said. "We meet with the conviction that human ingenuity can overcome the most daunting of challenges and we meet with the determination we will take the fight to dementia and improve and save millions of lives."
He added: "The aim of trying to find a cure or disease-halting therapy by 2025 by a big collective boost to research funding is within our grasp."
Jeremy Hughes, chief executive of the Alzheimer's Society, said: "Today the UK has demonstrated global leadership on tackling dementia. We have committed to a global plan, better support for people with dementia through research and the Prime Minister has agreed to narrow the funding gap between dementia and cancer research - something we have long campaigned for."
In the UK, about £590m is spent on cancer research, with £267m coming from Government.
An international investigation into the role of the neighbourhood in the everyday lives of people with dementia and their families was also announced yesterday by the Economic and Social Research Council and the National Institute for Health Research.
The five-year study will involve researchers from Stirling University along with colleagues from Manchester, Liverpool, University College London, Salford, Lancaster and Linkoping.
Dr Richard Ward, a lecturer in Dementia Studies at Stirling University, said: "Our research will add to a much-needed evidence base for dementia-friendly communities by helping us to understand how people living with dementia experience their local neighbourhoods."