"I will make clear at the next European Council in October that we must stick to the commitments we made in the June European Council," Mr Barroso said.
The Taoiseach raised fears that the economically powerful states of Germany, the Netherlands and Finland would fight an agreement to ease the debt burden.
Finance ministers from the three states said last month that they believed the June 29 summit had only settled on the European Stability Mechanism (ESM) covering the cost of future bank debt issues and not past problems which had already crippled some sovereign states.
Following a meeting on Ireland's upcoming European Union presidency, the Taoiseach warned: "That's not something we can put up with.
"This is about credibility, confidence and demonstrating to the citizens of Europe that when the council makes decisions in their interest that they are followed through.
"What's required here is pragmatic leadership, decisiveness and courage to implement the decision made in regard to the breaking of the link between sovereign and bank debt."
Mr Kenny is also keen to pursue plans for a banking union across Europe. He also committed Ireland to getting a single banking supervisor employed during its term, if not already in place. The official would be responsible for overseeing bank bailouts under the ESM.