Inflation was much hotter than expected, bad news for the Fed.

Prices continued to climb at a brutally rapid pace in September, with a key inflation index increasing at the fastest rate in 40 years, bad news for the Federal Reserve as it struggles to wrestle the cost of living back under control.

Overall inflation climbed 8.2 percent over the year through September, according to the latest Consumer Price Index report on Thursday, a slight moderation from August but more than what economists had expected.

Even more worrisome, underlying inflation trends are headed in the wrong direction. After stripping out fuel and food — which are volatile and removed to get a better sense of the trajectory — prices climbed 6.6 percent over the year through September. That was the quickest rate since 1982.

Inflation has been rapid for a year and a half now, and it is proving stubborn even as the Fed mounts its most aggressive campaign in generations to slow the economy and bring price increases under control. Fast inflation has also triggered the highest Social Security cost-of-living adjustment in decades — an 8.7 percent increase in benefits to retired and disabled Americans, a move that was announced Thursday.

Central bankers have quickly raised interest rates from near zero to a range of 3 to 3.25 percent, and investors expect a fourth straight three-quarter-point rate increase at the Fed’s next meeting, which concludes on Nov. 2. After the release of Thursday’s inflation data, they began to bet on another large move at the central bank’s December meeting.

“The trend is very troubling,” said Blerina Uruci, a U.S. economist at T. Rowe Price.

Markets swung wildly after the report, with stocks falling sharply initially but then surging higher as investors struggled to digest what the data meant for the future. The S&P 500 index closed up 2.6 percent.

Higher Fed rates are already slowing the housing market, and are expected to slowly filter through the rest of the economy as they make it more expensive to borrow money for big purchases or business expansions. But consumer demand is taking time to crack: With jobs plentiful and wages rising, Americans are still spending.

That is allowing companies to continue charging more. Lingering supply chain issues tied to pandemic-era shutdowns are keeping some goods in short supply, labor shortages are pushing up wages, and many corporations are raising prices by more than is necessary to cover their costs, finding that they can swell their profit margins without losing shoppers.

Inflation is also a stumbling block for President Biden and his fellow Democrats ahead of the midterm elections. The report on Thursday was the final Consumer Price Index release before the Nov. 8 elections, and Republicans wasted little time in excoriating Mr. Biden for his handling of the economy. While Americans are keeping up their consumption, many of the nation’s most vulnerable are struggling with rising food, fuel and housing costs — and most people are seeing their paychecks eroded by the cost increases.

Mr. Biden said the report showed “some progress” in combating the increases, noting that costs have climbed by less over the past three months than they had in the prior three months. But he also acknowledged that inflation remained painfully high.

“We have more work to do,” he said in a statement after the release.

Economists have predicted that the economy will slow and inflation will moderate in the months ahead. But they have been expecting an imminent cool-down for the past 18 months, and the data have repeatedly proved them wrong. Worried that rapid inflation might last, Fed officials have been clear that they plan to raise interest rates to a point where they are constraining the economy and hold them at a high level until price increases are clearly moderating. Officials have estimated that they will lift borrowing costs to about 4.6 percent by the end of 2023.

After making three unusually large rate increases, officials had suggested they would debate slowing down in November. The fresh inflation data makes another big move more likely, and economists said it could make it difficult for the Fed to slow down by the end of the year, as policymakers had previously forecast.

“It is hard to see how they build the case to step down the pace in December,” Ms. Uruci said.

It is too early to know how the Fed’s thinking will evolve by its final meeting of the year on Dec. 13 and 14. Even if inflation shows little sign of cracking by then, policymakers may want to give themselves time to see the cumulative effect of their rate increases, as well as fallout from monetary policy adjustments taking place around the world.

But for now, just about every sign they are receiving from the inflation data is discouraging.

Fed policy takes time to work, and most economists would not expect this year’s adjustments to be pulling inflation drastically lower yet. But because rate moves work by slowing consumer demand, one might expect their effects to show up in everyday consumer goods and services categories first. That has yet to happen. From restaurant meals to cigarettes to stationery products, prices continue to climb briskly, suggesting consumers are still willing to pay up.

And the duration of the price burst is troubling. Overall inflation has been above 5 percent for a full year now, far above the central bank’s goal. The Fed aims for 2 percent annual inflation on average, which it defines using a different but related gauge: the Personal Consumption Expenditures measure, which will not be released until late October.

As rapid price increases linger, central bankers fret that consumers and businesses will grow accustomed to them. If that happens, workers might begin to demand bigger pay increases to cover their climbing costs, and employers might make large and regular price adjustments a routine part of how they operate — making fast inflation a more permanent feature of the American economy and even tougher to stamp out.

Consumer inflation expectations have yet to budge much in surveys. But economists said there were signs in the inflation data itself that price increases might be growing more entrenched.

Housing costs, which make up a big part of inflation, have been rising steadily. Service industries like pet and dental care are posting big price increases, which could be a sign that the tight job market is pushing up wages and feeding into higher prices as companies try to cover their labor costs.

“We are starting to see persistent inflation creeping into the economy,” said Steve Rick, chief economist at CUNA Mutual Group. “We are really concerned about this turning into a wage price spiral, with wages rising and making it hard to get inflation down anytime soon.”

While wages are not climbing quickly enough to keep up with inflation, they are rising much more rapidly than is typical. Average hourly earnings for rank-and-file workers climbed 5.8 percent over the year through September. Those pay gains hovered around 2 percent or 3 percent in the decade leading up to the pandemic.

It is not just service costs increasing. Grocery bills were up across the board in September, with increases in the cost of fruit, vegetables and bakery products. The price of apples rose 5 percent from the previous month, while lettuce gained 6.8 percent and flour 2 percent.

Forces that economists had expected to temper inflation — including recent healing in tangled supply chains — are taking time to show up in the data. Used car prices were expected to decline sharply in this report, for instance, but fell only about half as much as anticipated. New car prices and car parts continued to rise rapidly as disruptions in those industries linger.

As a result, goods prices, which were expected to drag down inflation, instead neither added to nor subtracted from the data in September. Gas prices did weigh on overall inflation, which bodes badly going forward, since fuel costs have bounced back over the past month. Gas could switch from pulling inflation down to pushing it up by the next data release.

Those details illustrate what a sticky problem inflation has become for the Fed — and how painful it could be to resolve it.

The Fed’s policies work by making it more expensive to borrow money. As shoppers pull back and expansions become more costly to finance, businesses should hire less, the labor market should weaken, and wage growth should slow. That would reinforce the slowdown in demand.

That cycle takes time to play out — but because the Fed does not have the luxury of waiting in an environment of rapid and potentially re-accelerating inflation, officials have been adjusting policy aggressively without waiting to see the consequences. As it does so, the risk that the central bank will induce a punishing recession that tosses many people out of work has climbed. That would particularly hurt lower-income workers, who are vulnerable to job loss and who are already suffering the brunt of inflation.

“They have no choice but to try to get their arms around inflation,” said Mohamed El-Erian, chief economic adviser at Allianz. He said that the Fed was late in diagnosing inflation and too slow in reacting to it, and that he thought the economy would now pay for the central bank’s delay in responding.

“This is a self-inflicted wound that will impact the most vulnerable members of our society the most,” Mr. El-Erian said.

Joe Rennison, Ana Swanson and Tara Siegel Bernard contributed reporting.