Federal Reserve Bank of Minneapolis President Neel Kashkari said the U.S. central bank needs to tighten monetary policy until underlying inflation is declining, and then wait to see whether it has done enough.

“The one mistake that I’m acutely aware of—that I want to avoid repeating from the 1970s—is when policy makers saw the economy weakening, saw inflation start to tick down, and then they cut rates, thinking they had done the job. And then inflation flared back up again—that, I believe, is a mistake we cannot make and will not make,” Mr. Kashkari said Tuesday during an online event hosted by The Wall Street Journal.

The Federal Reserve has raised interest rates aggressively this year to reduce inflation, which remains near its highest rate in 40 years. The central bank last week approved its third consecutive interest-rate rise of 0.75 percentage point and signaled additional large increases were likely even though they increase the risk of recession.

The Labor Department’s consumer-price index rose 8.3% in August from the same month a year before, slowing from 8.5% in July and from 9.1% in June. But underlying, or so-called core inflation, which excludes volatile energy and food prices, climbed to 6.3% in August from its 5.9% rate in both June and July—a signal that broad price pressures strengthened.

Mr. Kashkari acknowledged that there is a “risk of overdoing it” but said he thinks the central bank is “moving at an appropriately aggressive pace” to tame inflation.

Fed officials have often said they want to produce a “soft landing”—slowing economic growth enough to reduce inflation without causing a recession. Mr. Kashkari said he thinks a soft landing is still possible, rather than a recessionary “hard landing.”

“We’re going to try and achieve a soft landing, but we are going to get inflation back down to 2%,” Mr. Kashkari said, referring to the Fed’s target of inflation averaging 2% over time.

Mr. Kashkari made the comments during a discussion on the economic outlook with former Treasury Secretary Lawrence Summers.

 Mr. Summers said a hard landing is more likely than a soft one.

“The likelihood is that the current Fed forecast—which is that both unemployment will peak at 4.5% and that we will get back to 2% inflation within 2½ years—I think the odds that both those things are going to happen together are probably less than one in four,” Mr. Summers said.