"A credit event, selective default or default must be avoided," Trichet told the daily Hospodarske Noviny, repeating the central bank's line two days before a eurozone summit on Thursday.
"We ask the eurozone governments to find appropriate solutions as soon as possible," he added.
The ECB chief dismissed calls for a Greek default as a way out of the crisis.
Richard Sulik, head of a junior party in Slovakia's coalition government and speaker of parliament, has been among those arguing that a default would help settle the Greek debt problem.
"Who could consider a default of any sovereign country, in the context of a European and global crisis of public finances, a good solution?" Trichet said.
Slovakia, which adopted the euro in 2009, was the only member of the currency bloc to refuse an emergency loan to Greece last year.
Its centre-right coalition, in power since July 2010, has suggested it might refuse to support a new loan as well.
Greece will be able to pay its bills this month after the eurozone cleared the way for the next 12-billion-euro tranche of last year's 110-billion-euro ($160 billion) European Union and International Monetary Fund bailout.
But the eurozone's finance ministers need to work on a second rescue package potentially of similar size to ensure Athens can stay afloat until at least 2014, warding off a devastating default that would reverberate across Europe.
"Membership of the eurozone brings many mutual dependencies that represent the advantages of a monetary union," Trichet said.
Other eurozone members that have found themselves under market pressure, such as Italy, will not need a bailout, he claimed.
"I am confident they are capable of reinforcing their credibility," he said.
Trichet said the ECB did not expect the debt crisis to cause a recession in the eurozone, adding the bank's governing council saw the risks as balanced.
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