By Anna Isaac and Alexander Osipovich

U.S. stocks rose on Monday, lifted by a surge in technology stocks like Apple and Microsoft, as well as signs that the rate of new coronavirus infections could be slowing.

The Dow Jones Industrial Average gained 201 points, or 0.8%, in morning trading, kicking off August with a modest uptick. The index climbed 2.4% in July. Trading volumes are expected to slide in coming weeks with the onset of the summer vacation season, leading to an increase in volatility.

The S&P 500 rose 0.7%, while the tech-heavy Nasdaq Composite climbed 1.3%, putting it on track for a fresh record.

Investors have piled into technology stocks in recent weeks. Robust earnings from tech companies and virus-fueled disruptions to traditional sectors, like airlines, retail and manufacturing, have widened the gap between Big Tech and everyone else.

Apple shares gained 3.6% on Monday. Microsoft shares climbed 4% after the software giant said over the weekend that it would move forward with plans to buy the U.S. operations of the hit video-sharing app TikTok. The companies' gains helped make tech stocks the best-performing sector of the S&P 500 on Monday.

Meanwhile, the U.S. registered its lowest number of new Covid-19 infections in weeks, spurring investors' hopes that the growth in cases could be slowing. The U.S. reported more than 47,000 new coronavirus cases, the smallest daily increase in almost four weeks, after posting a record number of new infections in the month of July.

"A couple of weeks ago, U.S. cases were rising by 40-50% on a weekly basis. They're now falling. Not as fast as they might appear, because testing has dropped, but they are still lower and so is the rate of hospitalization. Markets like that," said Ian Shepherdson, chief economist at Pantheon Macroeconomics.

New data showed U.S. manufacturing activity grew in July, a sign that the sector is still on a road to recovery after the Covid-19 pandemic forced much of the U.S. economy to an abrupt halt. The Institute for Supply Management's manufacturing index rose to 54.2 last month, from 52.6 in June. Economists had expected the reading to come in at 53.8. Anything above 50 represents an expansion in activity.

Overseas stocks rose after similar data pointed to a manufacturing recovery. The pan-continental Stoxx Europe 600 rose 2.2%, bolstered by survey data showing signs of recovery in euro area factories. In China, the Shanghai Composite Index rose 1.8% after a private gauge of manufacturing activity on the mainland rose in July to its highest level in more than nine years.

Investors were closely watching whether Washington would deliver a deal on further fiscal support for the American economy. Democrats and Republicans remained at odds in weekend negotiations on a new economic relief package, including aid to replace the federal $600-a-week boost to unemployment benefits that expired Friday. The White House had hoped to pass a short-term extension of the federal unemployment insurance, but Democrats want to negotiate a comprehensive package of relief, including state and local aid.

"The slowness with which Washington is coming to an agreement on a fiscal policy shows some fatigue. A deal will likely come, but after some big fiscal cliffs have been passed," said James McCormick, a strategist at NatWest Markets.

Secretary of State Mike Pompeo's comments over the weekend that the White House may take action against Chinese software companies stoked concerns about deteriorating relations between the world's two largest economies. Heightened tensions between Beijing and Washington have weighed on investor confidence for weeks, with growing expectations that the U.S. government will take a harder line in relations with Beijing in the run up to November's presidential election.

"It seems the closer the election gets, the fiercer tensions are likely to be," said Oliver Jones, senior markets economist at Capital Economics. "The China hawks in Washington appear to have the upper hand."

In corporate news, shares of ADT soared 71% after the security company said Google would invest $450 million to acquire 6.6% ownership in ADT, and the companies entered into a long-term partnership to create smart home security offerings.

Among European equities, HSBC Holdings slid 2.3% in London. The bank's second-quarter profit fell 96% as the disruption caused by the pandemic complicated its efforts to refocus on Asia while dealing with the rising U.S.-China political tensions. Siemens Healthineers fell 7.9% after the medical technology company said it would acquire Varian Medical Systems for $16.4 billion, or roughly 25% above its current market value.

The ICE Dollar Index, which tracks the greenback against a basket of other major currencies, ticked up 0.4% while remaining near its lowest level in over two years. The dollar had made a sharp U-turn this summer following a long rally, and its slide added further support to the booming market rally, lifting U.S. stocks and commodities.

In bonds, the yield on the benchmark 10-year U.S. Treasury ticked up to 0.556%, from 0.536% Friday.

--Frances Yoon contributed to this article.

Write to Anna Isaac at anna.isaac@wsj.com and Alexander Osipovich at alexander.osipovich@dowjones.com