Since the run on SVB that forced regulators to shut it down in mid-March, "things have kind of calmed down" in the banking sector, said Waller, who last week signaled that bank-sector calm is one reason he believes the Fed can and should continue to focus on fighting high inflation with further policy tightening. "That's the one thing about a bank run - it's a panic; once it stops, there's no real fundamental damage to the economy or the banking system per se."

The Fed is currently undertaking a review of what led to SVB's failure, and what policy fixes might be needed to avert a repeat. Waller's comments on the need for speed at the Fed's emergency lending "discount window" suggests one potential fix.

"If they are going to have deposit flows being faster we need to think how do we do pricing faster, how do we do assessment of the collateral, that's got to be faster -- that's one of the things I personally learned from this: to make the discount window more effective, we have to be able to do things faster as well," Waller said.

(Reporting by Ann Saphir; Editing by Chizu Nomiyama and Andrea Ricci)