The dollar index, which tracks the greenback against a basket of six major peers, last stood at 93.922. That was within sight of Friday's peak of 94.087, the highest for the dollar index since Nov. 21.
The Fed is widely expected to raise interest rates at its two-day policy meeting that will end on Wednesday and is expected to tighten policy further next year, although the policy outlook remains clouded by subdued inflation.
Since a rate hike this week has been priced in by the market, the dollar could sag initially after the Fed's policy announcement, said Steven Dooley, currency strategist for Western Union Business Solutions in Melbourne.
The Fed, however, will probably sound optimistic about the economic outlook and that is likely to help underpin the greenback, he added.
"Once the initial flurry of short-term volatility rides out, we're likely to see the US dollar stronger again," Dooley said, describing how the dollar could react to the Fed's policy announcement due on Wednesday.
"It seems most likely that the US Federal Reserve will continue to sound optimistic and certainly continue on the path to raise rates three times next year," Dooley said.
Against the yen, the dollar held steady at 113.56 yen , trading near Monday's high of 113.69 yen, which was the dollar's strongest level in about a month.
The euro last changed hands at $1.1775, having pulled back from Monday's intraday high of $1.1811.
The New Zealand dollar hovered near two-week highs on Tuesday as investors welcomed the appointment of national pension fund chief Adrian Orr, a former central bank official, to head the Reserve Bank of New Zealand from March.
Investors were relieved by the selection of an official with extensive expertise in monetary policy, and expected he would not veer too far from the status quo as he carries out a new dual mandate.
The New Zealand dollar held steady at $0.6911. On Monday, the kiwi had surged nearly 1.1 percent and climbed to as high as $0.6930, its strongest level since late November.
Bitcoin held steady near $16,470 on the Luxembourg-based Bitstamp exchange, having set an all-time high of $17,270 on the exchange on Monday.
Newly launched bitcoin futures on Chicago-based derivatives exchange Cboe Global Markets suggested that traders expect the cryptocurrency's blistering price gains to slow in the coming months, even as it blasted above $17,000 on Monday to a fresh record high in the spot market.