The Taoiseach has set a June deadline for a clear signal from the EU on reducing the burden in order to strengthen market confidence and lower rates as Ireland prepares to exit the bailout.
Mr Barroso expressed strong support for Ireland but refused to speculate on whether a deal would be done by the summer.
"This, I cannot predict how long is going to take, these technical discussions," he said.
Within government circles, there are genuine fears that no major progress will be achieved until after the German elections in September.
The European Commission chief's comments will have done nothing to ease those fears.
Mr Barroso and his team of European commissioners met with the Government at Dublin Castle at the start of Ireland's EU presidency.
Mr Kenny repeated his view that a deal on the Anglo Irish Bank promissory note would be done by March when the next repayment is due and a deal on the recapitalisation of AIB, Bank of Ireland and Permanent TSB would be done by June.
He also said a bank-debt deal was necessary for Ireland to successfully emerge from its bailout programme.
Mr Barroso said the European Commission was working hard to ensure that the link between sovereign and private debt is broken, but he could not predict when technical discussions would be finalised.
He urged EU member states to stick to the spirit of an agreement reached during a crucial summit last June – that the sustainability of Ireland's bailout programme would be improved.
"I was always making the case for the need for solidarity with Ireland and the need for fairness within Europe," he said.
"This is the commission's position in favour of fairness. You have the full support and the good will of the commission as you face the challenges ahead."
Mr Barroso said easing the country's bank-debt burden could only be achieved after the establishment of a single supervisory mechanism and that discussions on such a banking union were still continuing.
"Once this agreement is made we can proceed," he said.
"Technical discussions are still ongoing on how exactly recapitalisation will work. This, I can't predict how long is going to take."
The Government is hoping to use its six-month term in the EU presidency to push for a deal on €64bn bank-debt burden.
Mr Barroso insisted that the European Commission wanted to establish a direct recapitalisation instrument that breaks the link between sovereign and bank debt as soon as possible.
Mr Kenny welcomed the European Commission's commitment to Ireland.
"We do need the conclusion and the demonstration of assistance from our European colleagues," he said, adding: "I'm very glad President Barroso has referred to the issue of fairness."