In a letter marking the start of Britain's presidency of the Group of Eight richest nations, Cameron laid out his three priorities for the year: to extend free trade, tackle tax evasion and combat corruption.
Writing to the leaders of Canada, France, Germany, Italy, Japan, Russia and the United States, Cameron said: "It is clear that in 2013 the world will continue to face grave economic uncertainty."
While each country would rightly focus on their own challenges, he said, "the ambitious standards we set and the bold steps we take by working together through the G8 can make a tangible difference by firing up economies and driving prosperity, not just in our own countries, but all over the world".
But he warned that if the G8 is to see progress in these areas, leaders meeting in Northern Ireland in June need to do more than "whip out a chequebook at the 11th hour, pledge some money and call it a success".
"What we are talking about are long-term changes in our countries and the rules that govern the relationships between them. With ambition on this scale, I am convinced that success depends on us starting a debate on these changes now."
Cameron said the G8 nations, which together account for about half of global economic output, could offer leadership to ease trade negotiations, adding that the start of talks on a deal between the European Union and the United States would be "perhaps the single biggest prize of all".
The G8 could also "galvanise collective international action" to tackle tax evasion and avoidance by sharing information and looking at whether global standards need to be extended and tightened, he said.
And the prime minister urged the G8 to "put a new and practical emphasis on transparency, accountability and open government" in its relations with less developed and emerging economies, including by improving the way aid is spent.
Cameron added that he was reviewing why Britain had not yet signed up to the Extractive Industries Transparency Initiative, which is designed to shed light on who earns what from the exploitation of natural resources.
The United States was the only G8 country to have joined, he said, adding: "We need to change that. We cannot call on other countries to live up to these high standards if we are not prepared to do so ourselves."
The last time Britain held the G8 presidency was in 2005, when the summit at Gleneagles in Scotland was overshadowed by the bombings on the London transport system which left 52 people dead.