Investors around the world breathed a sigh of relief Monday after the U.S. government took over and backed Fannie Mae and Freddie Mac, assuring a continued flow of credit through America’s wounded mortgage system.

Stocks rallied in Europe and Asia, after the U.S. Treasury’s announcement that it would transfer control of Fannie Mae and Freddie Mac to conservatorship. Stocks in Tokyo closed 3.4 percent higher.

In Europe, the FTSE 100 index in London rose 3.7 percent at the opening while the CAC 40 in Paris registered a 4.3 percent gain and the DAX in Frankfurt 3.1 percent.

Futures contracts on the Dow Jones industrial average rose 2.2 percent in early European trading as investors concluded that the Bush administration’s decision over the weekend had strengthened the prospects for American businesses, particularly banks, and for the American economy.

Shares of major Japanese banks soared. Mitsubishi UFJ Financial rose 10 percent, while Sumitomo Mitsui Financial climbed more than 15 percent.

The dollar and yen weakened in orderly trading against the euro and the British pound in European morning trading, as investors halted a recent flight to the safety of the dollar and yen and began to conclude that European economies might not be in as grave danger as they had seemed last week.

German-listed shares of Fannie and Freddie plummeted in early Frankfurt trading, losing more than 50 percent of their value.

Investors said the provision in the bailout plan under which the Treasury will begin buying some of Fannie and Freddie’s securities in the open market would help to restore confidence.

“The fact that they’ll be able to buy mortgage-backed securities from other banks is really important,” William de Vijlder, chief investment officer at Fortis Investment Management in Brussels, said, “because it means the U.S. is serious about fixing the problems in the market.” The “doomsday scenario,” in which write-downs of those securities results in a continuing cycle of bank write-downs and losses, is over, he added.

“I expect a positive reaction in the market in the near term,” he said. “The problems have not gone away, but along with the decline in the oil price, this helps to put the machinery into place by which things will eventually return to normal.”

But the takeover of the companies also reinforced concerns about troubles of the American economy and highlighted its significant reliance on foreign investors, particularly in Asia.

Almost immediately, the move will protect central banks in Asia, which have amassed hundreds of billions of dollars of Fannie Mae and Freddie Mac bonds, from taking big losses. The move should also bode well for American financial institutions and, in the short term, the broader stock market.

Investors said they expected the spread between Treasury securities and comparable Fannie Mae and Freddie Mac debt to shrink drastically, reflecting renewed faith about the safety of the market.

In recent months that spread, or premium, had ballooned significantly, eroding confidence in the health of the companies. Before the housing crisis, Fannie and Freddie could borrow money at a small premium over the federal government’s rates. “If it becomes like U.S. Treasuries, that is a positive for Asia,” said Ifzal Ali, the chief economist of the Asian Development Bank in Manila.

Treasury’s purchase of mortgage securities may help lower interest rates on home loans, which this summer rose to their highest level in a year. That reduction in housing costs should help cushion the decline in home prices, which have already fallen more than 18 percent from their peak in the summer of 2006, said Bill Gross, the co-chief investment officer of Pimco, the large bond investment firm.

“It goes a long way to stopping this housing deflation which, I think and Pimco thinks, is at the heart of the problem,” he said.

But the plan also raises a host of questions about the fragility of the American economy, which will continue to figure into investor calculations. On Friday, for instance, the Labor Department reported that the unemployment rate climbed to a five-year high of 6.1 percent.

Perhaps most important, despite the government support for Fannie Mae and Freddie Mac, any stabilization in home prices is still a way off, and the waves of foreclosures battering the housing market are not likely to reverse right away. What is more, the plan will do little to stem losses in risky home loans, commercial mortgages and debt used by private equity firms to acquire companies. Financial institutions have already taken write-downs of $500 billion and the International Monetary Fund projects that losses could reach $1 trillion.

“It’s a good half a plan, but its still just half a plan,” said Joseph Mason, a finance professor at Louisiana State University, who cautioned that the government needed to outline its longer-range plan for the two companies and the credit markets to restore greater confidence to markets.

Yet for foreign investors, particularly in Asia, the takeover will do little to assuage mounting fears that the economic problems in the United States are not only far from over, but could also hurt growth in China, India and other emerging economies.

“People don’t know about the depth of the problem,” Mr. Ali said.

Asian central banks, particularly the People’s Bank of China, have emerged over the last several years as important buyers of bonds from Fannie Mae and Freddie Mac, the two American government-sponsored enterprises.

Standard & Poor’s estimates that the People’s Bank of China held $340 billion of these agency securities at the end of June, but has been unable to estimate Asian holdings over all because the data is too unclear.

While central banks around the world have historically accounted for a quarter of purchases of Freddie Mac debt, their share rose to 37 percent for debt issued since 2006, according to an analysis of the latest available data by CreditSights that was released on Wednesday. The bulk of those purchases appear to have been by Asian central banks, which have been buying dollar-denominated securities at a record pace to slow their currencies’ rise against the dollar and thus preserve the competitiveness of their exports.

Still, Asian central banks are likely to remain major buyers of mortgage securities. That is because they must reinvest dollars earned from exports to the United States, said Daniel Alpert, a managing director at Westwood Capital, an investment bank in New York. The Treasury backing of the debt will serve to make the bonds more attractive, he said.

“The money that they have been giving us as basically a gift will come back to them,” Mr. Alpert said, referring to the Asian investments in the mortgage securities. “They should be quite pleased.”