The country's banks are thought to be saddled with approximately €360bn (£304.7bn) of non-performing loans and it has been widely speculated that Renzi has recently been trying to arrange a capital injection for the sector with the European Commission, even though it would involve bending EU rules.
However, speaking with CNBC today, Renzi said:
I think the stress test show Italian banks as not the problem of European system... If you think about the last 12 months, every day we received a lot of news, the problem of our European system are Italian banks and our position was no, it's not true.
The recent European Banking Authority's stress test showed that troubled Monte dei Paschi's capital would have been entirely eaten away in the event of a sharp economic downturn.
Shares in Unicredit, meanwhile, had to be suspended yesterday after they plunged, as investors were clearly less than impressed when the bank ranked sixth worst in the financial health check-ups.
However, another Italian bank - Intesa Sanpaolo - was one of the shining stars of the stress test, being left with one of the more comfortable capital buffers should the worst happen.