The euro was trading at $1.4034 around 2200 GMT, up from $1.3897 late on Monday.
Against the Japanese currency, the dollar edged up to 80.64 yen from 80.49 yen on Monday.
The greenback has suffered heavily in recent weeks as traders anticipated the Fed would renew its asset purchasing policies, which effectively mean printing more money, in a bid to boost the lagging economic recovery.
The Federal Reserve's policy-making panel, the Federal Open Market Committee, began a two-day meeting in Washington. The FOMC was expected to announce its decision to unleash what is known as quantitative easing (QE) on Wednesday.
"While there will be some interest in today’s US elections, the next key event is of course the FOMC monetary policy announcement," said Wells Fargo analyst Nick Bennenbroek.
In late New York trade, the dollar fetched 0.9785 Swiss francs, down from 0.9913 on Monday.
The pound slightly rose to $1.6043 from $1.6042.