Trichet's comments at a conference in Cernobbio, on the shore of Lake Como near Milan, follow a stand-off over Europe's strong presence on the IMF board, with the United States pressing for more power for emerging countries.
In an interview with CNBC television on the sidelines of the Cernobbio meeting, Trichet also repeated remarks he made last week after the ECB left its main interest rate unchanged at 1 percent following a meeting of the governing council.
"The ECB has delivered price stability now it is up to the national governments to deal with competitivity issues," he said, noting that the economy had shown more positive signs over the past weeks.
"The probability of a double dip recession has decreased in the last few weeks," he said but added: "We can't say we have won, we have to be cautious and prudent to restore confidence and we will see what happens."
He also expressed confidence in the response by U.S. monetary authorities to the crisis.
"I am confident that the Federal Reserve will do what is necessary for the American economy."
In his remarks at Cernobbio, Trichet also repeated the ECB's longstanding line ruling out the possibility of Greece leaving the euro zone as a result of its debt crisis, saying a return to the drachma would be the worst option for Athens.
He said the bloc's stability pact had to be strengthened as much as possible, using "secondary legislation" because it would not be possible to change the treaty which created it.
He dismissed any suggestion that the euro needed to rival the U.S. dollar as a world currency.
"We created the euro to achieve the single market, for prosperity and stability of Europe," he said. "We did not create euro against the U.S. dollar, to compete with the U.S. dollar."
(Reporting by Francesca Landini and Ian Simpson; editing by James Mackenzie/Mike Peacock)
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