Trichet called for better monitoring of euro zone government budgets, which under the zone's stability and growth pact should run deficits of no more than three per cent of GDP.
"What we need is a quantum leap in mutual surveillance of economic policies in Europe. We need improved mechanisms to prevent and punish misconduct."
"We need an effective implementation of the mutual control, we need effective sanctions for breaches of the stability and growth Pact. The ECB calls here for profound changes."
Angela Merkel, the German Chancellor, warned on Saturday that the were the European monetary union to collapse it would "shake the whole European project" to its foundations.
"If the euro fails, a lot more will also fail," she told the Sueddeutsche Zeitung newspaper.
Stocks has rallied after last week's announcement that EU finance ministers had agreed to a $1 trillion package of loans and loan guarantees to prevent contagion.
But the optimism was short-lived, with the euro continuing to fall and stocks down three days this week.
"The euro hasn't derived any benefits from any budget cuts from Spain and Portugal," Chris Turner, the head of FX strategy at ING, told the Reuters news agency.
"People are either concluding that these cuts will be unsuccessful and debt sustainability remains a key issue, or they will be successful in aggressive fiscal tightening and that these economies would slow aggressively and the European Central Bank has to keep interest rates low."
ING forecasts that the euro will fall as far as $1.15 within six months.
The International Monetary Fund that budget deficits must be reined in to prevent economies contracting.
"As economies gradually recover, it is now urgent to start putting in place measures to ensure that the increase in deficits and debts resulting from the crisis ... does not lead to fiscal sustainability problems," it warned in a report on Friday.
"If public debt is not lowered to precrisis levels, potential growth in advanced economies could decline by over half a per cent annually, a very sizable effect when cumulated over several years."
The IMF said current policies could result in average debt ratios of 110 per cent of gross domestic product by 2015 for advanced economies