A new reading on inflation offers another challenge to investor expectations of a Federal Reserve rate cut in March.

A report out Thursday showed that consumer prices increased more than expected in December as the Consumer Price Index (CPI) rose 3.4% over the prior year, an increase from the 3.1% increase seen the month prior.

When removing the volatile food and energy categories, "core" inflation fell to an annual rate of 3.9% from 4.0% the month prior. Economists surveyed by Bloomberg had expected core inflation of 3.8%.

The numbers could complicate the task facing Fed officials, who predicted three interest rate cuts in 2024 without saying when they could happen. Investors expect six cuts this year, starting in March.

"Today's CPI report suggests that the Fed's initial rate cut may be later than the market is hoping for," said Quincy Krosby, chief global strategist for LPL Financial.

Several Fed officials offered their views following Thursday's report. Cleveland Fed President Loretta Mester told Bloomberg TV in an interview that March is probably too early for a rate cut and that the CPI report shows the central bank still needs to bring inflation down further.

Richmond Fed President Tom Barkin said he is still looking for conviction that inflation is on track to reach the Fed's 2% goal, while Chicago Fed President Austan Goolsbee said he also needs to see more data before cuts can begin.

Inflation, to be sure, continues to moderate following the most aggressive central bank campaign to cool prices since the 1980s. Core inflation has fallen to 3.9% from 5.6% at the beginning of last year.

The Fed last raised rates in July, to a 22-year high.

Read more: What the Fed rate-hike pause means for bank accounts, CDs, loans, and credit cards

Other Fed officials have also pumped the brakes on rate expectations recently. New York Fed President John Williams said Wednesday that he only sees cuts happening when the Fed is confident inflation is sustainably moving back to its 2% target — repeating a view he expressed in December.

"I expect that we will need to maintain a restrictive stance of policy for some time to fully achieve our goals," he said in a speech.

But he noted "significant progress" in a key measure of inflation known as "core services inflation," adding that shelter inflation is slowing as the growth of rents for newly signed leases returns to pre-pandemic levels.

Thursday’s CPI report showed the inflation measure less housing grew by 3.4% for December, while shelter itself grew at a slower pace of 6.2% versus 6.5% in November.