At 2100 GMT, the euro was at $1.2848, compared to $1.2758 on Monday.
The dollar fell against the yen, to 77.73 yen from 78.27 yen, while the euro was barely higher against the Japanese currency, rising to 99.88 yen.
Markets were focused on the ruling expected Wednesday by Germany's Constitutional Court on the legality of the European Stability Mechanism.
If it rules in support of the ESM, the eurozone will have fresh flexibility to deploy some 500 billion euros ($630 billion) to support the region's weakest members, with immediate attention on struggling Spain.
Also on Wednesday, the Federal Reserve's policy board starts a two-day meeting with expectations high that it will undertake new monetary easing measures, possibly a new quantitative easing (QE) program, that will push down long-term interest rates.
"As of right now, the market is pricing in positive outcomes for both events," said Neal Gilbert of currency specialists GFT.
The dollar slipped to 0.9392 Swiss francs from 0.9463 francs Monday. The British pound rose to $1.6067 from $1.5987.