The possibility of a 75 basis point rate hike in September was put on the table by Cleveland Fed President Loretta Mester on Friday.
In a speech to a European Central Bank Conference, Mester said she expects to support 50 basis point rate hikes at each of the Fed's next two meetings, which are scheduled for mid-June and late July.
The Fed can review the pace of further rate hikes at that point, Mester said.
If inflation isn't moderated by September FOMC meeting, the monthly readings on inflation provide compelling evidence that inflation is moving down, then the pace of rate increases could slow, but if inflation has failed to moderate, a faster pace of rate increases may be necessary, according to Mester.
A 75 basis point hike could come after the Fed's meeting on September 20 -- 21.
Earlier this month, Fed Chairman Jerome Powell said that a 75 basis point rate hike was not actively considered by the Fed.
Powell said in an interview with Marketplace Radio on Thursday that he wasn't taking a large move firmly off the table.
Economists said Powell was wrong to rule out such a big move because it raises questions about the Fed's willingness to get inflation back under control.
Mester is a voting member of the Fed's interest rate committee and is seen as one of the more hawkish regional Fed presidents.
The Dow Jones Industrial Average DJIA was up nearly 1.5% on Friday after six days of losses.
The yield on the 10 year Treasury note was under 3% for the fourth day in a row.