The crisis in Europe and a sluggish U.S. recovery have begun sapping growth across the rest of the world as China, India and other major developing countries join in an evolving global slowdown.

In its latest world economic projections, the International Monetary Fund sounded a newly cautious note about a situation where rounds of government stimulus spending and low interest rates have failed to take hold, and left countries saddled with debt and other problems that give them little room to maneuver if conditions get worse.

That has been the case for months now in Europe, and the fund has recently become more concerned about U.S. government debt and deficits as well.

The analysis released on Monday, however, highlighted the intensification of concern about the developing world — nations that had helped prop up global growth but which are now beginning to slow, and may be nearing crises of their own.

Overall, the world economy is still expected to expand by 3.5 percent in 2012 and 3.9 percent next year — only slightly less than fund economists forecast in April.

But the trend is in the wrong direction: Growth in the first months of the year was stronger than expected, and the slowdown in developing countries means the world is losing one of its few economic bright spots.

After the 2008 collapse of Lehman Bros., developing countries quickly lowered interest rates and pumped hundreds of billions of dollars of government money into the economy. Part of a coordinated global response encouraged by the United States, those efforts provided widespread help as Chinese companies and government agencies boosted equipment purchases from the United States and Germany, Spanish banks earned profits from their investments in Latin America, and Brazilian farmers benefited from record commodity prices.

The economic impetus from that effort, however, has begun to wane — a fact seen in Europe’s continued problems, ebbing U.S. growth, and a downturn in world trade that has begun to show up on the books of emerging market exporters.

Of perhaps more concern, the ability of governments worldwide to respond has become limited, the IMF said.

In China, India, and Brazil, for example, lending expanded so fast in recent years that the current economic slowdown could raise a new round of concerns about the impact that bad loans or falling asset prices would have on the financial health of banks.

China already has begun loosening credit and lowering interest rates in response to signs that its torrid rate of growth has ebbed — still forecast at 8 percent for 2010 but a full 2 percentage points below the pace of two years ago. But “expanding credit significantly at the current juncture would heighten asset quality concerns and potentially undermine GDP growth and financial stability in the years ahead,” the fund said.

In India and Brazil, policymakers had complained that a glut of dollars was driving up the price of the rupee and real. Now the opposite concern has taken hold as investors pull back in light of the slowdown. The currencies in those two countries have dropped sharply in recent months.

While an overvalued currency is troubling for a developing country because it makes exports more expensive, sharp swings down are bad as well — eroding the value of local investments and signaling that international investors may be losing faith.

The withdrawal of money from the developing world has not become critical — yet. But the IMF said it is worried that some of the world’s previous star performers could face a quick turnaround if conditions deteriorate.

“If and when a large downside shock ultimately materializes, these combined vulnerabilities could quickly come to the fore, putting financial stability to a serious test,” the fund concluded.