During his speech at the Central Bank Research Association on Thursday, Williams said his research showed that when interest rates are near zero, a central bank should "act quickly to lower rates at the first sign of economic distress".
The euro was 0.15% lower at $1.1258 after climbing 0.45% the previous day.
On Wall Street, a gain of 1.06% in Microsoft helped lift the Dow and kept the S&P 500 and Nasdaq slightly afloat as quarterly results topped expectations, powered by its cloud business.
The dollar index, which hit a two-week low of 96.648, bounced to 96.792.
While a spokesman later clarified that Williams was not outlining Fed policy and was not flagging a half-point cut, analysts said the remarks provided an insight into how officials were thinking.
Williams said when rates and inflation are low, policymakers can not afford to keep their "powder dry" and wait for potential economic problems to materialise.
While the United States economy is "in a good place", Clarida said recent global economic data have been softer than expected. Money markets are now pricing in a roughly 60% chance of a10 basis point rate cut next week, versus a 40% chance earlier in the week.
President Donald Trump slammed the Federal Reserve over interest rates and charged into confusion among investors caused by a speech from the central bank's NY branch.
Communicating the rationale for a larger cut could be tricky, because of the backdrop of relatively firm economic data, said William English, a former senior Fed economist who now teaches at Yale University. "The NY Fed went all the way to try to modify the message but no one seems to have done so for Clarida, who also said a very similar thing", said Daisuke Uno, chief strategist at Sumitomo Mitsui Bank. "One suspects that consumers and businesses will not like a non-uniform currency in which many types of currency trade simultaneously at a variety of prices in a local market".
The Stoxx Europe 600 Index increased 0.5%, the biggest climb in more than two weeks.
The Brazilian real rose to five-month high of 3.7172 to the dollar on Thursday while the South African rand also scaled a five-month peak of 13.8175 and last stood at 13.855. The market took this to mean that a bigger interest rate cut was on the way.
A vote by British lawmakers yesterday provided additional assistance to the Pound, however short lived.
There is no need, Bullard said, for the Fed to revisit current plans to continue letting government debt securities it bought to stimulate the economy after the 2008 financial crisis roll off its balance sheet without buying more bonds to replace them.
The softer dollar was also helping oil prices rally, while Donald Trump's claims that the U.S. had downed an Iranian drone that threatened an American naval vessel also provided strong support.