The narrowing in spreads between Italian and German bonds was encouraging them to spend more and feel less worried about their finances, he said.
Read MoreEurope's recovery depends on Renzi's Italy
"Now Italian people are feeling richer, because they have all their savings invested in government bonds, so they are coming back to consumption and there is clear evidence in the increase of industrial orders in the past months," he added.
Last week, data showed Italy's economy unexpectedly contracted in the three months to March and a decline in Italy's industrial production prompted concerns about the sustainability of the country's recovery for the year ahead. The data sent Italian stocks almost 4 percent lower. Intesa shares plunged as much as 6.2 percent. Intesa manages 800 billion euros owned by Italian families.
Commenting on the data, Messina said "investors were too reliant on Italian GDP figures".
Read MoreItaly: The next multibillion-dollar art market?
"First it was estimated to be up 0.2 percent for 2014 now it is -0.1 percent, at the end it is only statistical evidence and in our expectations the growth will be 0.5 percent. What is very important is the family recovery to consumption," he said.
"When investors will understand this point they will come to see the reduction of risk in the Italian situation. So I'm not worried at all on this point," he added.
The bank chief said the current round of European banking stress tests and the asset quality review has come at the "right time" and was very confident the bank would exit the exercise as "a clear winner amongst our European peers".
Read MoreItaly auctions off luxury cars… on eBay
When asked what his clients were most fearful of, he said that all eyes were on the European Central Bank meeting scheduled for June, which he said will give investors a real idea of what will happen in the real economy.
"In general my view is that they are waiting for the ECB actions. So the real turning point will be Draghi's conference. He can announce a quantitative easing program, and it's what I'm hoping to see, otherwise we'll only have a significant impact on financial economy and not on real economy," he said.
Clarification: This article has been changed to reflect that Intesa Sanpaolo manages 800 billion euros owned by Italian families.