Cleveland Federal Reserve President Beth Hammack said Monday that she believes more than one interest rate hike will be necessary to prevent inflation from becoming further entrenched in the U.S. economy.

Hammack made the remarks in an interview with Yahoo Finance, following her dissent from the Federal Reserve's decision to hold interest rates steady. She and two other members of the central bank's monetary policy committee voted in favor of a 25-basis-point rate increase. Three dissents at a single Federal Open Market Committee meeting are relatively uncommon, underscoring the depth of internal disagreement over the pace of tightening.

"I would say in general, one 25-basis-point move probably doesn't do a whole lot for the economy," Hammack said. "So it's probably some number of [movements]. But I don't want to prejudge what that number is going to be."

Hammack noted that she does not know exactly where the benchmark federal funds rate will ultimately settle, but she indicated that the current target range of 3.5% to 3.75% is not "meaningfully restricting" economic activity amid persistently elevated inflation.

"When I'm talking to businesses, I'm not hearing that they're sensing any restraint from investments in growth based on where interest rates are," she said. "So to me that says that now is the time to act."

Hammack warned that the longer the central bank waits to tackle inflation through tighter monetary policy, the harder it will be to bring price growth back to the Fed's 2% target.

Inflation has remained well above that goal. The consumer price index (CPI) rose 3.5% through June, while the Fed's preferred inflation gauge — the personal consumption expenditures (PCE) index — stood at 3.7% in June. The Fed tracks PCE more closely than CPI because it captures a broader range of household spending and adjusts for consumers shifting toward less expensive goods when prices rise.

Hammack drew an analogy to driving, saying that raising rates gradually is akin to easing on the brakes when approaching a stop sign to glide smoothly to a halt, rather than slamming the brakes with a more aggressive policy move to halt price growth.

"I think that now is the time for us to start acting, to start bringing more restraint into policy," she said.

"Nothing would make me feel better than to be wrong, that we need to change the stance of policy to help bring inflation back to target. But from where I sit, I just don't see it coming back on its own," Hammack added.

On the labor market, Hammack addressed the July jobs report, which showed a loss of 23,000 jobs — a sharp miss compared with economists' expectations of a gain of roughly 80,000. Despite the unexpected contraction, she said she is "still not seeing a problem" with employment conditions, citing the 4.1% unemployment rate, which she said is near her estimate of full employment.

Federal Reserve policymakers are scheduled to convene for their next meeting in mid-September. In the interim, they will have additional inflation data to evaluate, with the July CPI report slated for release on Wednesday and the July PCE reading due in late August. Those readings will factor into whether the committee moves toward the additional rate increases Hammack is advocating.