The dollar index was down at 79.176, not far from a near nine-month low of 78.998 touched on Friday. The longer the Fed keeps its policy loose, the more US yields stay anchored, making the dollar less attractive to hold.
In thin trade, the dollar's weakness saw the euro trade up at $1.3810, having risen to $1.3833 on Friday, its highest since November 2011 on trading platform EBS.
Investors are a bit wary of pushing the euro much higher, however, worried that policymakers at the European Central Bank may try to talk down the currency in coming days.
Speculation that ECB policymakers may talk down the euro has gained pace especially after recent economic data, including German business confidence and purchasing managers' index surveys, highlighted the fragile economic recovery.
"Eurozone policymaker concern is probably the biggest restraint for a euro/dollar that looks technically mobile toward the $1.3980/4000 area," said Tom Levinson, currency strategist at ING. "The dollar index looks primed for a test of support in the 78.60/90 area in coming days."
Most expect the Fed to express concerns about the economy, especially after the 16-day government shutdown that has hurt economic growth and hit business confidence.
With arch-dove Janet Yellen set to take over from Chairman Ben Bernanke the dollar is likely to struggle in coming months.
"The events in Washington have all but cemented the idea that tapering will be a 2014 event. Our economists' call is for April," said Adam Cole, head of G10 FX strategy at RBC Capital Markets, referring to the recent government shutdown.
"It seems likely that the upcoming statement will underscore the fiscal headwinds. A modest mark-down to the characterisation of the labour market also seems to be in order."
In fact, the implied yield on the Fed funds futures contract for December 2015 has fallen from a recent peak of 1.45 percent to 0.65 percent highlighting that investors have scaled back rate hikes expectations in 2015 and beyond.
While the dollar is likely to struggle against the euro and the British pound, it is likely to gain ground against the yen. The dollar rose 0.2 percent to 97.60 yen, edging away from a more than two-week low of 96.94 yen hit on Friday.
The dollar was supported on the view that yield differentials between Japanese government bonds and U.S. Treasuries will persist, as the Fed eventually moves toward tapering while the Bank of Japan keeps its ultra-easy stance.
The BOJ is widely expected to maintain its monetary policy stimulus at its policy review on Thursday to meet its target of two percent inflation in two years.
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