WASHINGTON – The weak U.S. economy, which has suffered thousands of job losses in recent months, may be on the verge of a rebound now that the Iraq war is over, the Federal Reserve said Wednesday.

The central bank said that four of its 12 districts — Dallas, Kansas City, New York and Minneapolis — detected signs of increased economic activity and no district reported further deterioration since the last report in late April.

“The unwinding of war-related concerns appears to have provided some lift to business and consumer confidence, but most reports suggest that the effect has not been dramatic,” the central bank said in its latest survey of business conditions.

The central bank cautioned against reading too much into the scattered signs of a rebound, describing overall activity in many districts as still “sluggish, subpar or subdued.”

The survey of business conditions, known as the beige book for the color of its cover, will be used by Fed policy-makers when they meet June 24-25 to set interest rates.

Many analysts are convinced that the Fed will cut rates for a 13th time at that meeting in an effort to make sure that the current weak patch the country is going through does not deepen into something worse such as another recession.

The conviction among analysts that the central bank is prepared to reduce its target for the federal funds rate, already at a 41-year low of 1.25 percent, has been strengthened by recent comments made by Fed Chairman Alan Greenspan. He has said the Fed would do whatever is necessary to guard against the remote possibility that economic activity in the United States will slow so much that deflation — a widespread fall in prices — could become a problem.

The United States has not been hit by a period of deflation since the Great Depression of the 1930s. However, the fact that Greenspan has even talked about the threat of deflation, remote as it might be, has been read as a strong signal that the central bank is ready to cut already low interest rates even further and keep them low for some time to come.

In a speech Wednesday, Federal Reserve Vice Chairman Roger Ferguson described the country’s near-term economic prospects as “still somewhat clouded.”

Ferguson, addressing the Japan Society in New York, said that recent readings on employment and industrial output have been disappointing. But he said there had been some encouraging signs as well in terms of declines in crude oil prices and a rebound in consumer confidence. He said a pickup in corporate earnings was helping to fuel a rebound in the stock market.

But Ferguson said, “Whether this improvement in overall financial conditions is a precursor to sustained recovery in the broader economy is unclear.”

The beige book said that consumer spending remained lackluster in May with retail sales rebounding with the end of the Iraq war but still remaining below the levels of a year ago. Many analysts believe consumer spending will remain depressed until the unemployment rate turns around.

The jobless rate hit a nine-year high of 6.1 percent in May, the government reported last week, even though the pace of layoffs slowed somewhat.

The Fed’s survey detected some improvements in the beleaguered U.S. manufacturing sector, which has suffered 34 consecutive months of job losses. Three districts — New York, Minneapolis and Cleveland — reported an increase in manufacturing activity while three others — Philadelphia, Richmond and Boston — indicated further deterioration. The remaining six Fed districts said there had been little change in industrial activity, which they reported remained sluggish.

The lowest mortgage rates in four decades continued to provide a boost to the housing industry with both home sales and residential construction posting further increases. But the survey found that commercial real estate remained in a slump.

The survey found that agricultural production was impaired by unusually wet weather in many parts of the country with rain delaying spring planting in the Atlanta, Chicago, Kansas City, Richmond and St. Louis districts.

At the opposite end of the spectrum, the Fed reported that crop conditions remained too dry in the Dallas district where farmers delayed planting their cotton crop because of insufficient moisture to germinate the seeds.

The decline in the dollar was helping U.S. exports, with the San Francisco Fed district reporting increased overseas demand for American beef and other farm crops because the falling dollar has made those products cheaper for foreign consumers.