The European bank, by contrast, is skeptical of the notion that inflation automatically falls when growth cools, and it has a mandate, inherited from the German central bank, to keep prices stable above all else. So the view from the European bank’s sleek silvery headquarters here is very different from the Fed’s perspective in Washington, whatever market participants may think about the inevitability of lower European interest rates.

Mr. Trichet is likely to drive home this point after the central bankers emerge from their monthly meeting here Thursday, when they are expected to leave rates unchanged at 4 percent.

Many investors remain convinced that the European bank has little choice but to follow the Fed’s lead, if only to ensure that recessionary conditions do not leach into Europe. As the Fed has cut rates, investors have bet that the bank here will follow and lower its benchmark rate, certainly by June and possibly earlier.

Image Jean-Claude Trichet seems to prefer a threat to a rise in rates. Credit... Sergio Perez/Reuters

The rise of the euro, which breached the $1.50 threshold last week and settled in New York Wednesday at $1.5262, also increases the pressure on the bankers from European politicians to at least hint at lower borrowing costs. Falling interest rates in the United States have exerted a powerful force on currency values by damping the appeal of dollar-denominated assets.

“In the present circumstances, we are concerned about excessive exchange-rate moves,” Jean-Claude Juncker, Luxembourg’s prime minister, who is presiding over the group of 15 euro-zone finance ministers, said on Monday.

But what sets off alarm among some politicians in Europe is far less likely to raise hackles at the central bank. That is because the euro’s rise also helps curb inflation by lowering the cost of imported goods. And if the euro’s appreciation is smooth, it supports the bankers’ decision so far to stand pat.