"I do not support stopping rate hikes unless we get clear evidence that inflation is moving down towards our 2% objective," Waller said in remarks prepared for delivery to a University of California Santa Barbara Economic Forecast Project event. "But whether we should hike or skip at the June meeting will depend on how the data come in over the next three weeks."

Particularly critical, he said, will be two more reads on inflation, as well as data on what is a "very tight" labor market and wages rising too fast to be consistent with stable prices.

Evolving credit conditions since the string of regional bank failures that began in March will also help inform his views, Waller said. "Between now and then, we need to maintain flexibility on the best decision to take in June."

But, he added, even if skipping a rate hike at the June 13-14 meeting is warranted, "prudent risk management would suggest skipping a hike at the June meeting but leaning toward hiking in July based on the incoming inflation data."

Earlier this month the Fed increased the target for its policy rate to the 5.00%-5.25% range, and Fed Chair Jerome Powell signaled that may be high enough for central bankers to pause their tightening campaign and assess the impact so far on the economy, especially given uncertainty over the outlook for credit conditions.

Waller's generally hawkish views on the need to act more forcefully against inflation helped drive the U.S. central bank's aggressive interest rate hikes last year. Core consumer inflation running at 5.5% is "too high" and the labor market, with 3.4% unemployment and hourly wage growth of 4.4%, needs to loosen to reduce price pressures, he said.

Waller's openness to possibly skipping an 11th straight rate hike next month given those concerns is notable, but so too is his view that the Fed may not be done yet.

By July, credit conditions will be clearer, and if banking conditions have not tightened excessively, "then hiking in July could well be the appropriate policy."