Many stock markets around the world rebounded Tuesday and early Wednesday after top officials of the U.S. central bank said they will probably keep interest rates at their current ultra-low level until the middle of 2013.

But continuing concerns about the U.S. economy and Europe’s debt problems drove U.S. and European stocks back down sharply on Wednesday.

The U.S. Federal Reserve’s record-low low interest rates are intended to make it easier to borrow money, expand businesses, and hire people.

The Fed said it took the action because of a downbeat assessment of the economy. Officials said they are worried that the nation’s economy is recovering more slowly and the labor market is weaker than expected.

Stock markets across Asia closed in positive territory Wednesday, mirroring the previous day’s big rebound on Wall Street from Monday’s massive sell-off. European indexes also made huge gains in the early hours of their trading sessions, but fell off sharply as the day progressed.

Tuesday’s U.S. Federal Reserve meeting followed several days of steep losses for stock markets around the world, and Friday’s downgrade of U.S. credit by the Standard & Poor’s rating agency. Central bank officials said they discussed other policy options to boost the economy, and are ready to use them if needed.