Before markets opened, the futures market had indicated a 1.3 per cent gain. However stocks then rallied and were up 1.4 per cent by late morning in New York. The Nasdaq Composite rose 1.2 per cent, recovering from a decline of almost 3.2 per cent.
The yield on two-year Treasuries, which is sensitive to changes in monetary policy expectations, surged 0.22 percentage points to 4.51 per cent, its highest level since mid-2007, before dropping back to 0.17 percentage points up on the day.
The persistence of high inflation has been a huge political headache for the White House and congressional Democrats, overshadowing a swift recovery out of the coronavirus pandemic with millions of jobs created since Joe Biden took office as president.
Senior White House economic officials initially expected the jump in inflation to be short-lived, then rushed to find ways to ease supply chain disruptions and reduce petrol prices, as the Fed began to tighten monetary policy.
Investors and economists had been looking for signs that the Fed might start to slow the pace of its interest rate rises from the 0.75 percentage point increases it has announced at each of its past three meetings.
But the CPI data released on Thursday suggest such a move is not yet on the immediate horizon.
Following the report, traders in the futures market priced in a 98 per cent chance that the Fed would lift interest rates by 0.75 percentage points in November, compared with 84 per cent on Wednesday.
Kathy Bostjancic, chief US financial economist at Oxford Economics, said consumer inflation remained "stubbornly elevated" due to "a continued broad-based surge" in prices for core services.
"High inflation readings will keep the Fed in an aggressive tightening mode and on course for at least another 125 basis points this year," she wrote in a note.
The futures market now expects the fed funds rate to reach 4.94 per cent by May 2023, up from 4.65 per cent the previous day. The central bank's policy rate is at present in a target range of 3 per cent to 3.25 per cent.
One of the most troubling features of the CPI report was that housing costs — described as "shelter" in the data — rose 0.7 per cent in September, as much as they had the previous month, and were up 6.6 per cent on an annual basis.
Amid intensifying political pressure, Biden eventually struck a deal with Congress to enact a legislative package called the Inflation Reduction Act, which included measures to reduce the cost of some goods such as prescription drugs, but had little effect on prices in the short term.
In a statement on Thursday, Biden acknowledged that Americans were "squeezed by the cost of living" and said there was "more work" to do to fight inflation even though some "progress" had been made.
He said that if Republicans take control of Congress "everyday costs will go up, not down".
Republicans have made rising prices a central part of their message to voters, blaming the Biden administration for the higher costs and tying the rise in prices to the Democrat-led stimulus enacted by the president in March 2021 that injected $1.9 trillion (NZ$3 trillion) into the US economy.
On Wednesday, several Republican lawmakers and candidates jumped on new figures showing that the producer price index, a measure of wholesale prices for businesses, rose faster than expected in September.
Rick Scott, Republican senator from Florida who chairs the National Republican Senatorial Committee, said inflation was an "unbearable kick for families trying to get back on their feet" in his home state in the wake of Hurricane Ian.
Mike Crapo, the most senior Republican on the Senate finance committee, said: "American families and businesses continue to be hammered by the runaway inflation generated from reckless spending policies of the Biden administration."
US consumers have received some relief from the fall in petrol prices that occurred over the summer. The peak of inflation under Biden so far came in June, when CPI rose 9.1 per cent on an annual basis. But the administration and Fed officials would have liked to have seen the price increases fade more rapidly than they have.
-By James Politi and Lauren Fedor in Washington and Kate Duguid in New York