The Prime Minister's move follows allegations that some of the world's largest companies, including Amazon and Starbucks, do not pay enough tax.
Following widespread public outrage the coffee giant announced at the end of last year it would increase the amount it paid in the UK.
But other companies, accused of underpaying to the tune of millions of pounds, have yet to follow their lead.
Mr Cameron makes his call in a letter to the leaders of the G8.
The UK is the new president of the international organisation and will host a meeting of the group in Northern Ireland later this year.
In his letter, the Prime Minister said he wanted the gathering to achieve a series of ambitious outcomes on international trade and aid as well as tax.
He wrote that to achieve such aims would take "strong political leadership" and months of work.
"This G8 will not be the kind of summit where we simply whip out a chequebook at the 11th hour, pledge some money and call it a success," he warned.
"What we are talking about are long-term changes in our countries and the rules that govern the relationships between them."
He told the leaders they had a common interest to ensure a crackdown on aggressive tax avoidance. But he warned they had to work together, saying "no one country can, on its own, effectively tackle" the issue.
He also urged the group to look at toughening the international standards that currently allow companies to decide where to declare their profits to reduce their tax bill.
He added: "The truth is that on all these issues, we know what the sticking points are and we need to find the political will to tackle them head on. By working together over the coming months, I believe that we can."
The move by Starbucks, which said it would pay £20 million to the Treasury over the next two years, is likely to increase pressure on other multinational companies at the centre of the storm.
But some of famous names have also hit back insisting they are doing nothing wrong.
Last month, Google chairman Eric Schmidt said he was "very proud" of the company's tax structure, and measures to lower its tax payments were just "capitalism".
Experts warn the global nature of change means an international solution has to be found.
Ministers are keenly aware they risk companies moving their business abroad if they crack down on tax avoidance without other nations implementing similar changes.
The G8 summit will see US President Barack Obama, Russian President Vladimir Putin, German Chancellor Angela Merkel and other world leaders gather for two days at the Lough Erne golf resort in Co Fermanagh.
It will be the first time the annual summit has been held in the UK since Gleneagles in 2005.
On trade issues, Mr Cameron said the new year offered the potential for a series of international agreements that could provide "vital opportunities" for global growth.
He also called for a crackdown on corruption in a number of nations.