Optimism about the fate of American International Group lifted stock markets on Tuesday, overshadowing lingering fears about other major financial firms and a stand-pat rate decision by the Federal Reserve that disappointed some investors.

The Dow Jones Industrial Average, which plummeted 504 points on Monday, recovered 141.51 points to end at 11059.02, up 1.3% for the day and down 17% for the year to date. Its component AIG fell 21.2% -- a relatively modest move compared to the 74% plunge it suffered at its intraday low....