The Fed’s favorite inflation index remains high in September.

Annual inflation is climbing at the fastest pace in three decades in the United States, according to data released Friday, keeping pressure on the Federal Reserve and White House as they try to calibrate policy during a tumultuous period marked by strong consumer demand and quickly rising prices for couches, cars and housing.

Jerome H. Powell, the Fed chair, has increasingly acknowledged that inflation is lasting longer than central bankers had expected. While Fed officials believe inflation will fade as supply chain snarls unravel and consumer demand for goods cools, it remains unclear when that will happen. Janet L. Yellen, the Treasury secretary, has predicted that rapid price jumps will cool by later next year.

Still, the current pace of inflation has become an uncomfortable political problem for President Biden and has created a delicate balancing act for the Fed, which is still trying to get the labor market back to full strength. Prices climbed by 4.4 percent in the year through September, according to the Personal Consumption Expenditures price index, which is the central bank’s preferred inflation gauge. That beats out recent months to become the fastest pace of increase since 1991.

Between August and September, prices climbed by 0.3 percent. That is in line with what economists expected and slower than rapid numbers posted earlier in the summer. Policymakers may take that as a sign that inflation was moderating, if still rapid on an annual basis, coming into the fall.

Friday’s data reconfirms what more timely inflation measures like the Consumer Price Index had already shown: Inflation continues to run at a rapid pace in the United States. That is happening in large part because supply chains are struggling to keep up with strong demand, thanks to virus-tied factory shutdowns, clogged ports and a shortage of transit workers, among other factors. The combination has made it hard to buy a kitchen table or a used car, and has caused the prices of many goods to jump sharply.

As prices climb, the Fed is preparing to slow down the large-scale bond purchases it had been using to lower long-term borrowing costs and support the economy. The central bank has been buying $120 billion in Treasury and mortgage-backed securities, but it is poised to announce its plan to slow that program as soon as next week. Mr. Powell has said buying could stop altogether by mid-2022.

That would leave the Fed in a position to raise its policy interest rate, its more traditional and arguably more powerful tool, should it need to do so to tamp down price increases. That rate has been set near zero since March 2020.

When the Fed raises interest rates, it makes it more expensive to borrow to buy houses, cars and washing machines. As demand cools, supply catches up and price gains moderate or even reverse, reducing inflation.

But the downside is that slower consumption and economic growth also lead to less business expansion and hiring. Slowing the job market is an unattractive prospect at a moment when millions of people remain out of work following lockdowns early in the pandemic and with concerns lingering about health and child care.

The Fed is closely watching measures of inflation expectations, which have risen in recent weeks, as it tries to assess whether price gains might jump out of control.

“The risk is that ongoing high inflation will begin to lead price- and wage-setters to expect unduly high rates of inflation in the future,” Mr. Powell said last week. And if inflation seemed likely to stay high, “we would certainly use our tools to preserve price stability, while also taking into account the implications of our maximum employment goal.”

The White House and broader administration are trying to make sure that concerns about prices do not undermine its economic agenda. Ms. Yellen said over the weekend that she expects inflation to ease by the middle of 2022.

“Americans have not seen inflation like we have experienced recently in a long time,” Ms. Yellen acknowledged on CNN’s “State of the Union” on Oct. 24. “As we get back to normal, expect that to end.”