The sovereign debt crisis has become systemic and risks to the economy are increasing swiftly, European Systemic Risk Board Chairman Jean-Claude Trichet said on Tuesday.

Trichet, who heads the European Central Bank as well as the continent's super-watchdog on financial stability, said the euro zone bailout fund should be made as flexible as possible, but without involving the ECB in leveraging it.

The crisis is systemic and must be tackled decisively, Trichet told the European Parliament's Committee on Economic and Monetary Affairs.

The high interconnectedness in the EU financial system has led to a rapidly rising risk of significant contagion. It threatens financial stability in the EU as a whole and adversely impacts the real economy in Europe and beyond.

Trichet called for governments and European authorities to act together to solve the crisis, adding that delay would be disastrous.

It is a matter of urgency that all authorities act in unison, with total commitment to safeguarding financial stability, he said.

The ESRB is designed to take a bird's eye view of Europe's financial system and flag up any emerging problems for relevant authorities to act on.

It has no formal teeth, although if it is not satisfied with authorities' reactions, it has the option of going public with its fears.

Trichet also called for a clear decision on recapitalizing banks and said the bailout fund could play an important role in this.

Supervisors must coordinate efforts to strengthen bank capital, including having recourse to backstop facilities, and also taking into account the need for a transparent and consistent valuation of sovereign exposures, he said.

The possibility for the EFSF to lend to governments in order to recapitalize banks -- including, if necessary, in non-program countries -- could be of benefit here, he said.

Commercial banks have become increasingly wary of lending to each other, more often turning now to the ECB for funding and deposits. Overnight deposits at the 17-country bloc's central bank shot up to 269 billion euros on Tuesday, the highest since June 2010.

(Reporting by Sakari Suoninen, editing by Mike Peacock)