NEW YORK - May 16, 2010 - After a brief respite following the announcement last week of a nearly $1 trillion bailout plan for Europe, fear in the financial markets is building again, this time over worries that the Continent’s biggest banks face strains that will hobble European economies.

In a sign of the depth of the anxiety, the euro fell Friday to its lowest level since the depth of the financial crisis, as investors abandoned the currency as well as stocks in favor of gold and other assets seen as offering more safety.

In trading early Monday morning, the euro declined again, managing at one time to reach a four-year low relative to the dollar.

The president of the European Central Bank, Jean-Claude Trichet, in an interview published Saturday, warned that Europe was facing “severe tensions” and that the markets were fragile.

For Europe’s banks, the problems are twofold. Short-term borrowing costs are rising, which could lead institutions to cut back on new loans and call in old ones, crimping economic growth.

At the same time, seemingly safe institutions in more solid economies like France and Germany hold vast amounts of bonds from their more shaky neighbors, like Spain, Portugal and Greece.