The Fed's Dudley cited "temporary, idiosyncratic factors" for weak prices and said "gradually" removing stimulus was still appropriate.
The Fed shouldn't wait until it reaches its economic goals before tightening monetary policy, Cleveland Fed President Loretta Mester said.
The Fed is getting more dovish in the face of weak inflation data, reducing the likelihood of a third rate hike this year, which traders already see as very unlikely.
Stocks in Asia declined on Wednesday as investors remained jittery about North Korea.
The market is focusing on inflation, but it's missing other signs a rate hike could happen sooner than it expects, Mohamed El-Erian said.
A Fed governor suggests the central bank will make an important shift in how it will approach rate hikes.
Lael Brainard is a member of the U.S. Federal Reserve's Board of Governors and a voting member of the Fed's policy-setting committee.
U.S. government debt yields were lower on Tuesday after North Korea conducted its most powerful nuclear test and key Fed speeches.