By Caitlin Ostroff and Juliet Chung

U.S. stocks wavered Thursday as weekly jobless claims held steady, pausing Wednesday's rebound after a recent technology-led sell-off.

The S&P 500 fell 0.3% midday, while the tech-heavy Nasdaq Composite Index was roughly flat. The Dow Jones Industrial Average was down 0.3%, while the pan-continental Stoxx Europe 600 fell 0.6%.

Big technology stocks were mixed, with Amazon.com Inc. up 0.7% and Netflix down 1.1%. Volatility in tech stocks has dominated markets in recent days. Tech shares rose broadly Wednesday following a three-session selloff that pushed the Nasdaq Composite into correction territory. Despite recent moves lower, the Nasdaq has gained more than 20% this year.

"The market was ahead of itself in the technology sector and it still is, " said David Bahnsen, investment chief for the $2.5-billion-in-assets wealth-management firm Bahnsen Group. He noted the Nasdaq had soared more than 60% from its March low. The recent reversal "doesn't mean all the froth has come out," he said.

Mr. Bahnsen said he had trimmed his clients' holdings in Apple Inc. over the summer and was readying, for the first time in a decade, to exit Apple entirely. He said he believed Apple was overvalued and its dividend, paltry, and said his clients' cash could find better value elsewhere. Apple was up 0.2% mid-day.

The recent slide in tech stocks has raised worries that the market, which had risen so sharply over the summer, could be set for a more turbulent period.

"We could see volatility continue just because there are so many factors if you think about the lack of progress on fiscal stimulus in the U.S. and the [Covid-19] case counts," said Wei Li, head of iShares EMEA investment strategy at BlackRock. "It's just hard to think we can put this to bed."

On Thursday, the government said about 884,000 Americans applied for unemployment benefits in the week ended Sept. 5, unchanged from the prior week. The labor market has gradually improved after the coronavirus pandemic struck this spring but new jobless claims remain at historically high levels.

Congress remains deadlocked over a fresh stimulus package. On Wednesday, Senate Republicans said they would support a scaled-back $300 billion version of their earlier $1 trillion stimulus plan, including jobless aid, liability protections for businesses and school funding. Democrats oppose the bill, and it isn't expected to clear its first procedural hurdle in the Senate on Thursday.

Quest Diagnostics was among the S&P's biggest gainers Thursday, climbing 4.1%. Shares in AstraZeneca were down 0.5%, despite the company's chief executive saying a Covid-19 vaccine it is developing with the University of Oxford could still be ready by the end of the year.

Electric-car maker Tesla Inc. was up 6% mid-day. Citigroup Inc. shares were flat; the bank announced Thursday Jane Fraser will become its next chief executive, marking the first woman to run a major Wall Street bank when Michael Corbat retires in February.

Tensions between Washington and Beijing continued to loom over markets. More than 70% of U.S. companies polled by the American Chamber of Commerce in Shanghai expect geopolitical turbulence to create operational difficulties for them over the next three to five years, up sharply from roughly half that said the same thing last year.

The euro was up 0.7% against the dollar after the European Central Bank said it would keep interest rates unchanged. ECB President Christine Largarde had an optimistic tone on the eurozone's stuttering economic recovery and the euro's strength.

In the bond market, the yield on the 10-year Treasury ticked higher to 0.717%, from 0.702% on Wednesday. Bond yields and prices move in opposite directions.

U.S. crude-oil futures edged down 0.6% to $37.83 a barrel. Prices have fallen lately with data indicating a slowdown in fuel demand at the end of summer and crude inventories rising.

Write to Caitlin Ostroff at caitlin.ostroff@wsj.com and Juliet Chung at juliet.chung@wsj.com