Trichet, who heads the European Central Bank (ECB) as well as the continent's super watchdog on financial stability, said the eurozone 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 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.
Recapitalising banks
Trichet also called for a clear decision on recapitalising 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 recapitalise banks - including, if necessary, in non-programme 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 €269bn on Tuesday, the highest since June 2010, indicating eroding trust between banks.
The leaders of Germany and France gave investors hope on
Sunday night by promising a plan soon to recapitalise Europe's banks.
However, investors remain cautious due to the lack of detail
about the plan, and the risk that a solution may be derailed by an event such
as political deadlock in Slovakia, the one euro country that has yet to approve
the EFSF expansion.
"The banking sector in Europe needs recapitalisation, that
is part of our message," Trichet said.
"Decisions have to be taken and taken very rapidly; I expect this decision to be taken as rapidly as possible."
Turning to the role of the European bailout fund, the
European Financial Stability Facility (EFSF), he said it could play an
important role.
"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 recapitalise banks - including, if necessary, in non-programme
countries - could be of benefit here," he said.
But while calling for the fund to be "as flexible as possible", he rejected using the ECB to leverage it, adding that governments had all the means necessary to leverage it without involving the central bank.