WASHINGTON — The world’s top central bankers have said they’re willing to rescue the economies of Europe and the United States. This week we’ll find out if they are ready to act.

The Federal Reserve wraps up its two-day policy meeting today. Chairman Ben Bernanke has pledged to act if unemployment stays high. The European Central Bank meets Thursday — a week after ECB President Mario Draghi vowed to “do whatever it takes” to save the European common currency, the euro.

“If the ECB comes through and follows up with what Mr. Draghi said a couple of days ago, that’s big,” says Nariman Behravesh, chief economist at IHS. “That would minimize the risk of a nasty scenario.”

Investors are hoping the Fed and ECB will announce plans to flood markets with cash through large-scale bond purchases. But economists caution that the hopes might be dashed. The Fed might not be in a hurry to act. And investors might be expecting more of Draghi than he can deliver.

Economies on both sides of the Atlantic need help. Unemployment in the 17 countries that use the euro remained at a record 11.2 percent in June, the European Union reported Tuesday. The International Monetary Fund expects the eurozone economy to shrink 0.3 percent this year.

The U.S. government announced last week that the American economy grew at a listless 1.5 percent annual pace from April through June, even slower than the 2 percent rate in the first three months of the year. On Friday, the Labor Department will reveal just how bad the American job market is. Economists expect the unemployment rate remained at 8.2 percent for the third straight month in July and that the economy generated just 100,000 jobs, not enough to keep pace with population growth. The first three months of 2012 job growth averaged more than 225,000 a month.