The Federal Reserve still has a lot of work to do before it gets inflation under control, and that means higher interest rates, San Francisco Fed President Mary Daly said Tuesday.

“People are still struggling with the higher prices they’re paying and the rising prices,” Daly said during a live LinkedIn interview with CNBC’s Jon Fortt. “The number of people who can’t afford this week what they paid for with ease six months ago just means our work is far from done.”

Separately, Chicago Fed President Charles Evans opened up the possibility of another large rate hike ahead, but said he hopes that can be avoided, with the Fed being able to bring down inflation without having to use harsh policy tightening.

So far this year, the central bank has raised its benchmark interest rate four times, totaling 2.25 percentage points. That has come in response to inflation running at a 9.1% annual rate, the highest level since November 1981.

The Fed in July raised its funds rate 0.75 percentage point, the same as it hiked in June. Those were the largest back-to-back increases since the central bank started using the funds rate as its chief monetary policy tool in the early 1990s.

But Daly cautioned that no one should take those big moves as an indication that the Fed is winding down its rate hikes.

“Nowhere near almost done,” she said in assessing the progress. “We have made a good start and I feel really pleased with where we’ve gotten to at this point.”

Futures pricing indicates the markets see the Fed raising rates by 0.5 percentage point in September and another half percentage point through the end of the year, taking the funds rate to a range of 3.25%-3.5%, according to CME Group data. That scenario holds that the economy would slow due to the policy tightening, and the Fed would start cutting rates by next summer.

But Daly pushed back on that notion.

“That’s a puzzle to me,” she said. “I don’t know where they find that in the data. To me, that would not be my modal outlook.”

Evans, her Fed colleague, also spoke Tuesday morning, saying the central bank is likely to keep its foot on the brake until it sees inflation coming down. He expects policymakers to raise rates by half a percentage point at their next meeting in September, but left the door open to a bigger move.

“Fifty [basis points] is a reasonable assessment, but 75 could also be OK,” he told reporters. “I doubt that more would be called for.” A basis point is 0.01 percentage point.

“We wanted to get to neutral expeditiously. We want to get a little restrictive expeditiously,” Evans added. “We want to see if the real side effects are going to start coming back in line … or if we have a lot more ahead of us.”

However, he also said he’s hopeful that policymakers could soon pause the rate hikes as inflation comes down.

Neither Evans nor Daly are voting members this year on the rate-setting Federal Open Market Committee, though they do participate in policy sessions.

The FOMC does not meet in August, when it will hold its annual symposium in Jackson Hole, Wyoming. Its next two-day meeting is next month, Sept. 20-21.