WASHINGTON — Federal Reserve officials must choose this week between their best estimates and their worst fears of what will happen to the US economy.

Policy makers will bring new forecasts to their Tuesday-Wednesday meeting and probably will mark down their April central-tendency estimate for growth of 2.4 percent to 2.9 percent this year. Lurking in the background is the risk of increasing financial stress in Europe and stubbornly high US unemployment that has remained above 8 percent for 40 consecutive months.

All this could prompt them to move away from their outlook for moderate growth and tilt toward a ‘‘risk-management’’ strategy pioneered by former Fed chairman Alan Greenspan, which puts more emphasis on tracking and containing high-cost threats. Both Janet Yellen, the Fed’s vice chairwoman, and William C. Dudley, head of the Federal Reserve Bank of New York, used the phrase in the past month.

Federal Reserve officials see a greater chance of a downturn than they do of inflation, said Donald Kohn, the former Fed vice chairman who is now a senior fellow at the Brookings Institution. ‘‘In a situation like this, their reasoning is you might want to buy some insurance.’’

That insurance may come in the form of extending Operation Twist — which JPMorgan Chase & Co. and Jefferies & Co. predict — or an even more aggressive response if Fed officials see high costs in a slowdown of US growth. The $400 billion program, which was announced in September and ends this month, involves selling short-term debt and buying longer-term bonds.

The Fed has about $190 billion of short-term maturities left to continue Operation Twist for another three months, based on calculations by Nomura Securities International Inc. The firm’s forecast is for no extension at the June meeting, with both chairman Ben Bernanke and the Federal Open Market Committee probably indicating they could take additional easing steps, such as outright bond purchases, if economic circumstances warrant.

An extension would fit a forecast that says the US economy will avoid a disaster scenario of rising unemployment and rapidly decelerating inflation. The Fed’s decision Wednesday could be more aggressive than investors expect if policy makers decide their confidence in their own forecasts is low and want to do something extra to lean against a worst-case scenario, said Vincent Reinhart, chief US economist in New York at Morgan Stanley.

‘‘We put high odds on them acting at the meeting,’’ said Reinhart, who was the head of the Fed board’s Division of Monetary Affairs, which develops policy strategy. ‘‘Risk management says that you act in advance of a potential downdraft in activity because that could trigger’’ a collapse in demand that would be difficult to escape with the main policy rate at zero. The Fed cut the target for the federal funds rate to a record-low range between zero and 0.25 percent in December 2008.

Greece’s largest pro-bailout parties, New Democracy and Pasok, won enough seats to forge a parliamentary majority, easing concern the country was headed toward an imminent exit from the euro. Even so, optimism about the election quickly faded as Spain’s 10-year bond yields rose above 7 percent to a euro-era record.

In the United States, payrolls increased by just 69,000 jobs last month, and unemployment rose to 8.2 percent from 8.1 percent in April. Still, few private-sector economists are forecasting another recession.

The United States will grow between 2 percent and 2.5 percent in each of the remaining three quarters this year, according to the median estimates in a Bloomberg News survey in early June.