By Paul Vigna and Anna Hirtenstein

U.S. stocks waffled Thursday after Federal Reserve Chairman Jerome Powell said the central bank would abandon its policy of pre-emptively raising rates to head off inflation.

The Dow Jones Industrial Average was recently up 76 points, or 0.3%, paring an earlier advance of more than 300 points. The S&P 500 lost 0.1%, a day after the stock index set its fourth straight record close. The technology-heavy Nasdaq Composite Index fell 0.7%.

Speaking remotely during the Federal Reserve's annual symposium, Mr. Powell unveiled a new strategy in which the central bank will tolerate periods when inflation runs higher than 2% to even out periods when it has been below that mark.

"Basically, they're telling you, 'We're not going to short-circuit this economy,'" said Keith Lerner, a strategist at SunTrust Advisory Services.

Markets swirled after the speech as investors tried to digest its ramifications. Gold rose, and then fell. Bond yields fell, and then rose. Stocks futures were largely negative, but the major indexes opened higher, before coming under pressure again,

Ultimately, Mr. Lerner said, the market will reposition for higher long-term inflation expectations.

The moves are also coming after an unusually strong summer for equities. The S&P 500 was on pace for its 15th positive day this month. That would put it up 79% of the days this month, according to Dow Jones Market Data. That is the highest percentage since February 2017, and if the index were to close out the rest of the month higher, it would be the highest since May 1990.

Although investors expected the Fed's shift in inflation targeting, the focus on the Fed's other mandate -- employment -- was a bit surprising, said Merk Investments analyst Nick Reece.

The Fed's goal isn't necessarily to have the unemployment rate hit any specific target, but to have an economy that coaxes "marginal" workers back into the labor force.

"They're trying to bring unemployment down, and the labor-force participation rate up," Mr. Reece said. One way the central bank can affect that is by not raising rates when inflation levels hit 2%.

The yield on 10-year U.S. Treasury note rose to 0.740% from 0.686% on Wednesday, extending this week's multiday selloff in U.S. government bonds. Bond prices and yields move in opposite directions.

Additionally, while long-term bond yields rose, short-term bond yields fell. That kind of development is good for banks, which generally borrow short-term and lend long term. Consequently, the S&P 500's financial sector was up 1.4%, the best of the index's 11 sectors. JPMorgan gained 2.7%, and Bank of America edged up 1.6%.

For equities, the upshot of the Fed's new policy is that the relative value of stocks should be higher than bonds, Mr. Lerner said. "It will continue to push investors into riskier assets if they want to get any kind of return."

Among individual stocks, Walmart, up 4.4%, and Microsoft, up 1.9%, were the Dow's two biggest dollar-gainers. That came after Walmart said it discussed joining Microsoft in a bid for Chinese-owned social media app TikTok's U.S. operations, and after TikTok Chief Executive Kevin Mayer resigned from the company, citing the political environment as the Trump administration tries to force a sale.

Cloud software company NetApp rose 4.9% after reporting stronger-than-expected results late Thursday. Abbott Laboratories added 7% after receiving emergency-use authorization from the U.S. Food and Drug Administration for its rapid-response coronavirus antigen test.

In economic news, the number of Americans applying for jobless benefits fell modestly last week, in line with economists' expectations for a small decline. About 1.006 million people applied for benefits in the week that ended Saturday, compared with 1.106 million in the previous week and economists' forecasts of 1 million.

"While this is much in line with expectations, it doesn't change the fact that politicians need to pass something," said Michael Hewson, a markets strategist at brokerage CMC Markets, referring to the need for further stimulus. "The likelihood is that joblessness will start to push higher. The longer it goes on, the pressure to do something will increase."

Negotiations between the Republicans and Democrats on another coronavirus aid package have stalled, which some analysts worry will eventually threaten the rally in stocks.

Overseas, the pan-continental Stoxx Europe 600 fell 0.6%. In Asia, benchmark stock indexes were mixed. The Shanghai Composite Index advanced 0.6%. South Korea's Kospi index fell 1.1% after its central bank cut its GDP growth forecast for 2020.

Write to Paul Vigna at paul.vigna@wsj.com and Anna Hirtenstein at anna.hirtenstein@wsj.com