The Dow Jones industrial average rose 69 points to close at 13,323.
Germany's high court will decide Wednesday whether the country can participate in a European bailout fund.
Many expect the Fed will launch a new effort to revive the sluggish economy after it wraps up its meeting Thursday.
The Standard & Poor's 500 index rose four points to 1,434. The Nasdaq lost one point to end at 3,105.
Two stocks rose for every one that fell on the New York Stock Exchange. Trading was in line with the recent average at 3.4 billion shares.