Not having a deal on the promissory note will make re-entering the markets "much more difficult".
Mr Kenny is confident Ireland can strike a deal easing the terms of the Anglo Irish promissory note by March.
He said he expects Ireland to return fully to the bond markets late next year but needs a deal on easing our bank debt to make sure we can successfully exit the international bailout.
The Taoiseach highlighted the importance of the Irish Bank Resolution Corporation (IBRC) promissory note issue.
"A deal on this would certainly make it so much easier for Ireland and enhance our ability to get back there.
"Not having a deal on the promissory note would make it so much more difficult," he said.
Mr Kenny said bank-related debt was a "burden" on the Irish economy.
"It will be absolutely crucial for confidence in our own economy here and will also help unblock credit for businesses and for investment directly into the economy," he said.
"As I have said on many occasions our aim is to re-engineer the IBRC promissory note by March so, if you like, change from a very special overdraft agreed to be paid down quickly to a much cheaper longer term loan."
Mr Kenny also called on European leaders to stick to a separate promise to address the cost of Ireland's bailout programme.
"We would hope to be the first country to actually exit (a bailout) in 2013 but that level of support that has been committed to Ireland is very necessary to be carried through," he said.
"This assistance and this support is very necessary for Ireland to exit the programme," he said, adding that the Government would not need to seek a second bailout.
Mr Kenny said he envisaged a sustained return to debt markets in the second half of 2013, adding a deal on the €31bn of promissory notes would help this greatly.
"It would be much easier to do that if we have a conclusion to the matter of the promissory notes and ECB negotiations which would obviously make it easier for us to have a full return to the markets... probably in the second half of the year," he said.