By Anna Hirtenstein

U.S. stocks paused Tuesday ahead of the first debate between President Trump and former Vice President Joe Biden before the November presidential election.

The S&P 500 ticked down less than 0.1%, suggesting stocks may struggle for traction. The broad-market index closed up 1.6% on Monday, rising for the third straight day. The Dow Jones Industrial Average lost 0.1%, while the tech-heavy Nasdaq Composite Index was roughly flat.

Volatility in markets is on the rise with the U.S. election around the corner. The two candidates will face off at 9 p.m. ET in Cleveland, Ohio, to discuss their respective records, the coronavirus pandemic, the economy, race and violence. Other issues are likely to be their views on mail-in voting, interference by overseas interests and potential election fraud.

"People will read into this debate for answers to questions about whether the results of the election will be accepted by either side," said Tony Dalwood, chief executive of Gresham House Asset Management. "If there's any uncertainty around this, that will lead to volatility."

Investors are also continuing to assess the now-dimming prospects for new additional spending to support the government.

House Democrats released a $2.2 trillion-bill for a coronavirus-relief package on Monday evening. House Speaker Nancy Pelosi is likely to speak to Treasury Secretary Steven Mnuchin about it on Tuesday morning. But the focus in Congress has turned to the selection of a new Supreme Court justice, analysts said.

"A combination of the situation with the Supreme Court, and Democrats being unwilling to hand Trump a major fiscal stimulus just before the election, makes it quite unlikely that we'll see something passed," said Sebastian Mackay, a multiasset fund manager at Invesco.

Investors are also awaiting a gauge of U.S. consumer confidence from the Conference Board, which will be out at 10. a.m. ET. Consumer spending is the biggest driver of economic growth in the U.S. The latest data could provide some insight into the sustainability of the recovery in the absence of more government support.

Overseas, the pan-continental Stoxx Europe 600 declined 0.3% as coronavirus cases continued to rise, raising the risk of more stringent measures being introduced by governments in the region. The U.K.'s FTSE 250 index was the worst-performing in Europe, slipping 0.9%, as investors got increasingly jittery about the Brexit negotiations.

In Asia, major stock benchmarks were mixed by the close of trading. The Shanghai Composite Index advanced 0.2% and Hong Kong's Hang Seng Index slipped 0.9%.

The dollar continued to weaken, extending its decline over recent days. The WSJ Dollar Index, which measures the dollar against a basket of currencies, edged down 0.2% to its lowest level in nearly a week.

In bond markets, the yield on the 10-year Treasury fell to 0.650%, from 0.661% on Monday.

Ahead of the opening bell in New York, shares of Abbott Laboratories rose 2.4% after Mr. Trump said 150 million rapid coronavirus tests made by the pharmaceutical company would be shipped across the U.S.

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