But the euro won some relief on Monday after weaker-than-expected U.S. manufacturing, industrial output and housing data pushed down U.S. debt yields and cooled the dollar's advance.
The U.S. currency's surge since early March has been driven by solidifying expectations that the Fed's Open Market Committee (FOMC) will point towards a June rate rise by dropping a pledge to be "patient".
The dollar has gained around 20 percent against a basket of major currencies over the past six months and some investors speculate that the Fed cannot ignore how much that rise reduces pressure on inflation.
Derek Halpenny, European head of global markets research at Bank of Tokyo-Mitsubishi UFJ in London, reckoned the removal of the word "patient'' was "pretty much a done deal'', but that investors were nevertheless eager to take risk off their books ahead of the Fed meeting.
"There are so many other angles that (Fed Chair Janet) Yellen could go at to paint a picture of caution and the potential for the first move to be beyond June,'' he said.
"If you've been short euro over the past week, you've had a good week, and why would you bother running the risk into what is a difficult event to predict?''
Having hit a 12-year low of $1.0457 at the start of the week, the euro was up 0.2 percent at $1.0589 on Tuesday morning. The dollar was around 0.1 percent lower against a basket of major currencies.
Traders will also keep an eye on how other asset markets react to the Fed's statement and comments from Yellen after the meeting.
"The main point is how Treasury yields respond to the Fed. Despite the removal of ''patience``, prospects of a September, rather than June, rate hike may linger, given the dollar's appreciation and lower oil prices,'' said a currency trader at a large Japanese bank.
The dollar inched up 0.1 percent to 121.42 yen, stuck in a relatively narrow range since advancing to an eight-year high of 122.04 on March 10.
The Bank of Japan concluded its two-day policy meeting on Tuesday, at which the central bank stood pat on monetary policy and maintained its massive stimulus. Market reaction was limited because the outcome was as expected.