The dollar edged down against its major counterparts in Asian trading Tuesday, though it remained in a relatively narrow range amid investors' caution ahead of this week's U.S. Federal Reserve meeting. The dollar was at 96.80 yen, down from 97.15 yen in late North American trading on Monday. The dollar index , a measure of the greenback against a trade-weighted basket of currencies, was at 79.19, down from 79.365 late Monday. The euro traded at $1.4164, up from $1.4135 late Monday. Looking ahead, investors await the outcome of the Fed's monetary policy meeting on Tuesday and Wednesday. Analysts expect little change to officials' statement about leaving interest rates unchanged for an extended time. The Fed is also widely expected to allow its program of buying up to $300 billion in Treasurys to expire when that amount is reached, likely sometime in September.