Italy and Greece are the key problems facing the euro zone despite much focus being on the continent's busy election schedule this year, according to Axel Weber, the chairman of Swiss bank UBS.

The sustainability of public finances has not yet been achieved in Greece, warned Weber, speaking to CNBC from the IMF's (International Monetary Fund) annual Spring meeting in Washington, D.C. on Saturday.

"That's a problem that is not resolved – it's off everyone's radar screen," he pointed out.

Similarly, Italy's weak economic and financial situation is set to be a bigger elephant in the room than the outcomes of this year's Dutch, French and German elections, all of which have seen populist candidates gain significant momentum and attention.

"The real tail risk is the Italian situation because … Italy has not grown for almost two decades now. So whilst in the U.S. the crisis is a remote memory, in Europe it is still the acute presence," argued the long-tenured banker, explaining that this dynamic is set to determine the populist agenda in Europe in a way that the U.S. has managed to avoid.

Weber highlighted the continually diverging fortunes of European countries, noting that while German output is exceeding even pre-crisis peaks, other countries such as Italy and Spain are still wracked by economic turbulence.