STORY: Schein said her comments brought some relief to investors, who have mostly been hearing Fed members talk of continued aggressive rate hikes to curb inflation.

Given that markets have priced in a monetary policy setting that's well beyond what the Fed has imposed on the economy so far, Daly said "it will be important to remain conscious of this gap between the federal funds rate and the tightening in financial markets. Ignoring it raises the chances of tightening too much."

That said, the Fed's policy rate is currently in "modestly restrictive" territory and "there is more work to do" to get monetary policy in the right place to cool inflation, Daly said a speech before the Orange County Business Council in California.

The San Francisco Fed chief is not currently a voting member of the rate-setting Federal Open Market Committee, which will almost certainly raise its policy rate next month, the only question being by how much.