Throughout the speech Barroso gave three main examples - fairness in global trade, fairness on tax and fairness on transparency over how revenues from oil and other natural resources are used and on what companies are paying to governments.
Mr Barroso said the EU was "pioneering the global agenda" on these issues at the top of the G8 agenda and explained the steps Europe has recently taken, including far-reaching proposals on cross-border exchange of tax information and new EU laws to increase transparency in large companies' accounts.
Later, Presidents Barroso and Van Rompuy joined US President Barack Obama and the G8 host, UK Prime minister David Cameron to launch the negotiations for a transatlantic trade deal.
Speaking of the deal, Mr Barroso said: "Our joint endeavour is part of our overall agenda for growth and jobs on sides of the Atlantic by boosting trade and investment. It is also a powerful demonstration of our determination to shape an open and rules-based world.”
"We intend to move forward fast. We can say that neither of us will give up content for the sake of speed, but we intend to make rapid progress."