"We are diversifying our government bond portfolios and we will have to because going under the ECB (European Central Bank) it's better to have a diversified government bond portfolio," CEO Carlo Messina told an analyst call.

He said this could mean selling some Italian government bonds and instead buying debt issued by higher-rated euro zone countries such as Germany and France.

Italian banks have increased their domestic bond holdings massively during the sovereign crisis, helping the Treasury meet its funding needs even as foreign investors shunned the country's debt.

Rising returns on Italian and other lower-rated peripheral euro zone bonds as the debt crisis eased have helped boost banks' profits in recent quarters.

The ECB will take on the role of single supervisor for the euro zone's banking sector in the autumn.

($1 = 0.7450 Euros)

(Reporting by Silvia Aloisi, writing by Valentina Za, editing by Isla Binnie)