Mr. Waller said Wednesday’s inflation report, in which the Labor Department reported the consumer-price index rose 9.1% in June from a year before, was “a major league disappointment.” The CPI index rose at the fastest pace in more than 40 years and revealed a broadening in price pressures even after accounting for large gains in food and energy prices last month.

But he said he nevertheless thought an increase of 0.75 percentage point, or 75 basis points, would be appropriate later this month, in part because of signs that the economy appeared to be slowing. “You don’t want to overdo the rate hikes. A 75-basis-point hike, folks, is huge,” Mr. Waller said at a conference in Victor, Idaho. “Don’t think because you’re not going 100, you’re not doing your job.”

Mr. Waller said he would consider supporting a larger rate rise if reports due Friday morning on retail sales and consumers’ inflation expectations and later this month on housing activity show “demand is not slowing fast enough to get inflation down.”

Fed Chairman

Jerome Powell

said last month the central bank was likely to consider raising its benchmark federal-funds rate by either a half percentage point or 0.75 point at the July meeting after raising it by 0.75 point in June, the largest increase since 1994.

In recent weeks, most officials had signaled they would favor the 0.75-point increase, and since Wednesday’s report, officials have conceded the debate is likely to shift toward whether to consider a larger, full-point increase. The Fed hasn’t raised interest rates by a full percentage point since it began using the fed-funds rate as its primary tool for setting monetary policy in the early 1990s.

Fed officials are set to begin their premeeting quiet period on Saturday, leaving little time to shape expectations around their monetary-policy plans.

Three Fed officials who spoke Wednesday didn’t say whether they would favor such a move, but they didn’t rule it out. “Everything is in play,” Atlanta Fed President

Raphael Bostic

told reporters in Florida.

A fourth official, San Francisco Fed President

Mary Daly,

told the New York Times she was leaning toward a 0.75-point increase but that a larger rate rise was possible.

St. Louis Fed President

James Bullard

said Wednesday he continued to favor a 0.75-point rate rise in an interview published Thursday by Nikkei Asia.

After Wednesday’s inflation report, investors in interest-rate futures markets and some analysts judged that the central bank would approve a one-percentage-point rate increase at its meeting in two weeks. The probability of a one-point increase rose to around 80% on Wednesday, up from around 12% before the inflation report, and then dropped to around 40% on Thursday, according to CME Group.

“The markets may have gotten ahead of themselves a little bit yesterday,” Mr. Waller said Thursday. “We don’t want to make snap policy decisions based on some knee-jerk reaction to what happened in the CPI report.”

U.S. interest-rate expectations are volatile partly because the Fed made a surprising shift in June. Most officials at the central bank had provided specific guidance that the Fed would raise rates by a half-percentage point at the June meeting ahead of their premeeting quiet period. But the CPI report released days before the meeting pointed to a worsening outlook, prompting the Fed to make the larger 0.75-point rate increase.

Mr. Waller said by raising the fed-funds rate by 0.75-point this month, which would lift it to a range between 2.25% and 2.5%, the Fed would be close to a neutral rate that neither stimulates nor restricts demand.

Mr. Waller said he expected further rate rises would be needed after that to slow demand for products and labor to bring down inflation. While some commentators have suggested that the neutral rate is higher because inflation is so far above the Fed’s 2% target, Mr. Waller said that thinking “rests on a flawed idea of how monetary policy affects spending decisions.”

Because spending decisions that require debt are based on an outlook that extends several years, Mr. Waller said it was better to think about a neutral interest rate that is tied to the expected path of both interest rates and inflation over the next several years.

At the same time, Mr. Waller pushed back against critics who are worried the central bank is overdoing rate increases. Even if inflation is being aggravated by supply bottlenecks and other issues outside of the Fed’s control, he said the central bank couldn’t distinguish between the causes of inflation.

Write to Nick Timiraos at nick.timiraos@wsj.com