By Anna Hirtenstein

U.S. stocks fell again Thursday, following data showing hundreds of thousands of Americans continue to tap jobless claims in the midst of the coronavirus pandemic.

The data helped drag the S&P 500 down 0.1% in early-morning trading. The Dow Jones Industrial Average also fell 0.1%, or about 40 points, while the Nasdaq Composite swung between small gains and losses.

Thursday's moves follow a 2.4% drop for the S&P 500 on Wednesday, knocking the benchmark down to its lowest level in almost two months. Losses continue to pile up, putting the stock market's rally since March on hold as investors fret over whether the U.S. government will funnel further stimulus aid into the economy.

At the same time, coronavirus infections continue to rise in many parts of the world, including the western U.S. The presidential election campaign season is fueling volatility: President Trump on Wednesday wouldn't commit to a peaceful transfer of power after the November vote. He predicted that the outcome would be decided by the Supreme Court, a reason he wants to quickly fill the vacancy left by the death of Justice Ruth Bader Ginsburg.

Federal Reserve officials on Wednesday stepped up calls for additional fiscal relief to bolster the economy. Chairman Jerome Powell and his colleagues said Congress and the White House, more than the Fed, had the power to hasten a faster recovery.

"America sneezes and the rest of the world catches a cold: if you're being told that the world's largest economy will not recover without stimulus and they can't agree on a stimulus, then that has to be a negative piece of news," said Tony Yarrow, a multiasset fund manager at Wise Funds. "The mood among investors is extremely pessimistic at the moment."

Mr. Powell is scheduled to offer congressional testimony in Capitol Hill for a third day this week and will speak Thursday morning. He is expected to give an overview of the economy and monetary policy, which could provide clues into the central bank's actions going forward.

In bond markets, the yield on the benchmark 10-year Treasury edged down to 0.664%, from 0.676% on Wednesday.

The latest data on new jobless claims for the week ended Sept. 18 showed that the number of workers applying for jobless benefits rose to 870,000, compared with 866,000 last week.

"This week's rise in initial jobless claims will come as a surprise to the market," said Richard Flynn, U.K. managing director at Charles Schwab. "Despite some encouraging numbers in recent weeks, the level of weakness remains unprecedented, and the labor market's recovery will likely rely on further fiscal support from the government."

Daily new coronavirus cases in the U.S., which began to trend downward in mid-July, have also been going up since mid-September in a worrying sign for investors.

The timeline for a coronavirus vaccine being widely available also remains unclear: Dr. Anthony Fauci, the nation's top infectious-disease expert, expects to see data from Phase 3 clinical trials of some candidates indicating whether the vaccines are safe and effective by "November or December" of this year.

In contrast, Mr. Trump has repeatedly claimed that a vaccine will be available before the early November elections. On Wednesday, he appeared to criticize forthcoming Food and Drug Administration guidelines being developed around the release of a vaccine, adding to concerns that the health issue was being politicized.

Overseas, the pan-continental Stoxx Europe 600 dropped 1.1% as investors weighed the prospect of stringent measures being introduced in countries such as Germany, France and the U.K. following a rise in infections.

"We all assumed restrictions would be over by September, but it turns out that we're in September and we're being promised another six months of dislocation," said Mr. Yarrow. "Everyone's having to reset their expectations."

In Asia, major benchmark stock indexes closed lower as the negative sentiment spread overnight. The Shanghai Composite Index retreated 1.7%, and Hong Kong's Hang Seng Index fell 1.8%.

-- Michael Wursthorn contributed to this article.

Write to Anna Hirtenstein at anna.hirtenstein@wsj.com