The euro was trading at $1.4636 around 2100 GMT, up from $1.4572 late Monday in New York.
Against the Japanese currency, the dollar slipped to 81.55 yen from 81.82 yen Monday.
The US unit tumbled to an all-time low of 0.8745 Swiss francs before regaining ground, trading late Tuesday at 0.8754 francs compared with 0.8808 francs Monday.
The pound fetched $1.6465, rising slightly from $1.6493 the prior day.
‘The dollar ended today's session on a weak note as a broad-based rally in global equities bolstered risk appetite after the extended holiday weekend,’ said Michael Woolfolk at Bank of New York Mellon.
Nick Bennenbroek, head of currency strategy at Wells Fargo Bank, predicted further dollar weakness after the Fed's policy-setting Federal Open Market Committee winds up a two-day meeting Wednesday.
‘Market participants continue to lean towards further US dollar weakness and global currency strength and will be looking towards tomorrow's FOMC announcement to confirm those inclinations,’ he said.
‘Markets expect little to no change in the Fed's policy stance, an outcome that should allow for further greenback declines.’
The FOMC is widely expected to maintain interest rates at between zero and 0.25 percent, where they have stood since December 2008 in a bid to support recovery from recession.
US Treasury Secretary Timothy Geithner vowed Tuesday that the United States would never follow a strategy to weaken the dollar.
‘Our policy has been and will always be, as long as I will be in office, that a strong dollar is in the interest of the country,’ Geithner told a New York conference organized by the Council of Foreign Relations.
‘We will never embrace a strategy to weaken the dollar.’
It was the first time this year that Geithner had publicly proclaimed a US strong-dollar policy, a mantra of treasury secretaries for more than a decade.