* U.S. financial system 'starting to heal' - Geithner
* Fed cuts outlook for U.S. economy
* Japan's economy shrinks record 4 pct in Q1
* Economy still getting worse, downturn slowing - Zoellick
* EU, China agree to work together against crisis
By Wanfeng Zhou
NEW YORK, May 20 (Reuters) - The U.S. financial system is healing, Treasury Secretary Timothy Geithner said on Wednesday, but contractions in Japan's and Mexico's economies showed the path to a global recovery could be long and tough.
The U.S. Federal Reserve said it saw modest improvements in the U.S. economy last month, but cut its forecast for economic growth over the next three years.
World Bank President Robert Zoellick was equally cautious, telling a meeting of regional central bankers in Finland that the global situation was still getting worse but "we are likely to see the rate of decline lessen."
Geithner said the U.S. financial system was "starting to heal" after a time of severe trauma, thanks to the government's bailout efforts, and that a program for cleansing toxic assets from banks will start over the next six weeks.
"We still face a very challenging economic and financial environment, and we need to be careful to preserve substantial resources and flexibility to deal with future contingencies," Geithner told the Senate Banking Committee.
Despite some modest improvements, the Fed gave a more pessimistic view of the world's largest economy, projecting a contraction of 1.3 to 2.0 percent this year and a rise in the unemployment rate to between 9.2 and 9.6 percent.
U.S. Treasury debt prices rose after minutes from the latest Fed policy meeting in late April showed officials discussed buying more securities, including government debt, to help spur the economy.
"Fed officials judged the financial system to be vulnerable to further shocks," said John Canavan, analyst at Stone and McCarthy Research Associates in Princeton, New Jersey.
JAPAN AND MEXICO SUFFER
Earlier Wednesday, Japan said its economy, the world's second largest, contracted by 4 percent in the January to March quarter from the previous three months and by 15.2 percent from a year earlier as capital spending sank at the fastest pace on record and private consumption fell the most since 1997.
By comparison, the U.S economy shrank 1.6 percent in the first quarter, or 6.1 percent on an annualized basis, while the euro zone economy contracted 2.5 percent.
With Japan heavily reliant on exports, economists said a lasting recovery will depend on how soon the global economy recovers and demand in the West grows.
"The export plunge is spreading to domestic demand," said economist Hiroshi Shiraishi at BNP Paribas. "As such, the Japanese economy may return to growth temporarily but it could suffer a contraction again afterwards."
Mexico's economy -- also very dependent on exports -- suffered a sharp decline in the first three months of this year, shrinking 5.88 percent from the previous quarter and 8.2 percent from a year earlier.
Finance Minister Agustin Carstens warned that Mexico, which ships about 80 percent of its exports to the United States, could see its economy contract 5.5 percent this year.
Analysts see the current recession rivaling Mexico's mid-1990s financial meltdown known as the Tequila Crisis.
In another sign of the need for cooperation, the European Union and China patched up differences at a summit, pledging to create a new global order to combat the financial crisis, shrinking world trade and climate change.
"We both recognize that it is important for us to work together, to ride out the storm and make our contribution to an early world economic recovery," said Chinese Premier Wen Jiabao.
Officials in China have grown increasingly confident that an 8 percent expansion can be achieved this year with the help of Beijing's stimulus package and said extra measures would be taken to maintain the momentum of a recovery.
U.S. HOUSING IS KEY
Wall Street stocks fell on the Fed's outlook and as financial shares were sold off after recent rises, running contrary to gains in many Asian and European markets.
The dollar fell to its lowest mark in nearly five months against the euro and a basket of currencies as the view that the worst of the global slump may be over dented its safe-haven appeal.
Oil firmed above $61 a barrel after data showed U.S. crude stocks fell more than expected in the week to May 15.
The U.S. economy may not emerge from its slump until the housing market stabilizes, economists say.
A Reuters poll found the U.S. housing market, the source of the global financial crisis, is edging closer to a bottom but the timing of a turnaround is highly uncertain.
The Mortgage Bankers Association said demand by Americans for mortgages to buy a home fell last week but overall applications rose, reflecting more interest in refinancing loans as interest rates drop.
The collapse of Spain's housing sector, coupled with a jobless rate of 17 percent, led to a larger-than-expected contraction in its economy in the first quarter.
Worries about the global recession also continue to put pressure on corporate earnings.
Deere & Co, the world's largest maker of agricultural machinery, reported sharply lower quarterly earnings as weaker crop prices weighed on demand for tractors and harvesters. Deere also cut its full-year earnings forecast again. (Reporting by Reuters correspondents worldwide; Writing by John O'Callaghan; Editing by Eddie Evans)