With core inflation still hovering around 2.75% and GDP growth projected to slow to about 1% this year, Williams said the Fed’s current policy stance of holding rates between 4.25% and 4.50% remains "entirely appropriate".

While almost no one thinks Donald Trump's verbal attacks on Federal Reserve Chair Jerome Powell are a positive development, they have electrified the debate about whether the U.S. president is right that interest rates are too high.

Some investors had clung to a bit of hope that the Federal Reserve would cut interest rates at its next meeting on July 30. Tuesday's report on inflation brought the chances of that down even further.