European Central Bank President Jean-Claude Trichet warned policy-makers from around the world on Saturday not to forget the lessons of the devastating financial crisis now that the worst has passed.

Now that we see some signs confirming that the real economy is starting to get out of the period of 'free fall' -- which does not mean at all that we do not have a very bumpy road ahead of us -- the largest mistake we could make would be to forget the importance and the urgency of this task, Trichet told fellow central bankers at a Federal Reserve conference.

Speaking at the closing session of the two-day annual retreat, Trichet -- who at the same conference last year was fretting about inflation only weeks before investment bank Lehman Brothers collapsed -- urged his peers to do everything they could to prevent a repetition of such dramatic events.

Trichet and other central bankers, meeting in the shadows of Wyoming's majestic Grand Teton mountains, took cautious note during the conference of signs suggesting the worst of a devastating economic storm was over, while promising to rebuild fractured financial systems to better withstand future crises.

Officials this year gathered with a noticeable sense of relief after two conferences dominated by the financial panic, which has now largely subsided.

However, they tempered their optimism with a discussion of the difficulties that lie ahead, including the tricky question of how and when they should pull back the massive amounts of support they have provided economies to combat the financial meltdown and a painful recession.

Huge budget deficits from enormous fiscal stimulus packages were another cause for concern.

U.S. stocks ended the week at 2009 highs on Friday after a surprising rise in home sales and optimistic comments from Fed chief Ben Bernanke reassured investors about the prospects for an economic recovery.

Opening the conference, Bernanke gave his clearest signal yet that the global economy is emerging from a recession. But he warned growth would be sluggish for a time.

ECB Governing Council member Ewald Nowotny said on Saturday the European economy will improve in the second half of this year, driven by policy measures, but a sustained recovery will likely not take hold until the beginning of 2010.

One worry for many policy-makers is whether the United States can reverse its aggressive programs that have flooded the ailing economy with cash in time to avoid inflation.

A paper presented at the conference argued the Fed's stated intention to keep interest low for an extended period could be incompatible with its goal of keeping inflation down, a conclusion rebutted by Fed Vice Chairman Donald Kohn.

Speaking for this policy-maker, the commitment to low rates is designed to keep inflation from falling and falling persistently below what we might want it to be for a long time, Kohn said. It's not designed to raise inflation expectations.

The Fed chopped benchmark U.S. rates to near zero in December and has pumped hundreds of billions of dollars into the economy to help boost economic activity and turn back a deep recession that began in December 2007.

Kohn also defended the Fed's decision to buy long-term securities as emergency measures to spur growth after it had cut interest rates as far as it could. Economists, including officials at the Fed -- the U.S. central bank, have questioned how successful those purchases have been in lowering rates.

Another ECB official told participants that the ECB was not likely to deviate from its inflation targeting strategy, and warned that pulling benchmark euro zone rates down to near zero, as the Fed has done, could unsettle markets.

The zero lower bound may interfere with the functioning of financial markets, thereby upsetting the stimulative impact of very low rates, said ECB Executive Board member Juergen Stark.

The ECB is expected to keep rates on hold at a record low 1 percent at its September policy meeting as it waits to see the impact of efforts already undertaken to revive the euro zone economy and spur credit flows.

Some economists have criticized the ECB for moving less aggressively than the Fed to spur economic activity. In defense, Trichet said central banks must build and guard a reputation for moving interest rates steadily and persistently to be most effective.

Such deliberate and persistent moves strengthen transmission, thereby proving effective in achieving our objective of price stability, he said.

That approach contrasts with that of the Fed, which aggressively cut rates in 2007-2008 as the financial storm gathered strength.

(Additional reporting by Kristina Cooke; Editing by James Dalgleish)