BRUSSELS (Reuters) - The European Union could consider setting up a European Monetary Fund and making banking supervision independent from the ECB to better protect the bloc from future financial crises, the head of the euro zone bailout fund said.

However, these plans would take place only in the event of EU treaty changes, said European Stability Mechanism director Klaus Regling.

Regling also said that were treaty changes made, the EU should consider taking away from the ECB its supervision power over the euro zone banking sector.

The financial support and economic policy monitoring of euro zone countries is now carried out jointly by the European Commission, the European Central Bank and the ESM, the common bailout fund.

Merging their functions into a single institution would bring the euro zone closer to having a European version of the International Monetary Fund, Regling told a conference in Brussels. This would help the 19 countries of the currency union to better weather future financial and banking crisis.

He stressed that this could be done only with a change to the EU treaty, a lengthy and open-ended process that member states are wary of embarking on.

But if the process of changing the treaties were initiated, "one could take some of the functions that are now split over three different institutions into one, to have also in one building a European Monetary Fund," Regling told the Brussels Economic Forum, a gathering of EU financial leaders.

He said a more urgent task for the euro zone was to complete the banking union, a project meant to increase financial stability in the bloc.

The project, already under way, is now stuck on the setting up of a common insurance scheme for banks' deposits, which Germany opposes. Germany fears an increased sharing of risks would disproportionately expose its banks to weaker lenders in other European countries.

Should treaty change be made, the EU should consider taking away from the ECB its supervision power over the euro zone banking sector.

Currently, this function is played by the Single Supervisory Mechanism, a recently established body which is within the ECB.

Regling suggested "taking the SSM out of the ECB to make a real, independent banking supervisory authority."

(Reporting by Francesco Guarascio; Editing by Keith Weir)