Chicago Federal Reserve President Charles Evans said the central bank is holding fast in its commitment to bring down inflation even if it means people losing their jobs.

Speaking three weeks before the Fed is expected to approve its fourth consecutive 0.75 percentage point interest rate increase, the central bank official told CNBC he hopes to minimize economic damage.

"Ultimately, inflation is the most important thing to get under control. That's job-one," Evans said during a live "Squawk on the Street" interview. "Price stability sets the stage for stronger growth in the future."

Markets will get a fresh look at producer and consumer price indexes later this week. Both have been showing cost-of-living increases near their highest levels in more than 40 years.

On the employment front, the Bureau of Labor Statistics reported Friday that nonfarm payrolls increased 263,000 in September, while the unemployment rate fell to 3.5%, tied for the lowest level since late 1969. However, Fed officials including Chairman Jerome Powell have warned that they expect ";some pain" from the Fed's inflation-fighting efforts that could include higher levels of joblessness.

"If unemployment goes up, that's unfortunate. If it goes up a lot, that's really very difficult," Evans said. "But price stability makes the future better."

The Fed faced a renewed bout of criticism Monday from ARK Investment Management founder Cathie Wood. In an open letter to policymakers, the ETF manager said she is worried that interest rate hikes are based on backward-looking data and could send the economy into a "deflationary bust."

Evans said he sees some signs that inflation is letting up as supply chain pressures ease. He advocated a policy stance where the Fed gets rates to a restrictive level at which point it can monitor the impact.

Evans is a non-voter on the rate-setting Federal Open Market Committee and has said he is leaving his position early in 2023.