By Anna Isaac

U.S. stocks open mixed Monday as major equity benchmarks look to close out their best month since April.

The S&P 500 edged down less than 0.1%. Last week, the S&P 500 logged its strongest performance since early July, putting its advance so far in August at about 7.2%.

The Dow Jones Industrial Average fell 0.2%, while the technology-heavy Nasdaq Composite Index gained 0.1%.

Both the S&P 500 and the Nasdaq index notched all-time highs at the end of last week as the summer-vacation season began drawing to a close. Optimism was buoyed by a shift in the approach to monetary policy from the Federal Reserve, which has signaled that it is likely to keep U.S. borrowing costs down for an extended period.

"They've confirmed lower-for-longer rates as far as the eye can see," said Richard Dunbar, head of multi asset research at Aberdeen Standard Investments. "Alongside that confirmation of cheap money and cheap discount rates, we've just come through a U.S. earnings season that's been a lot better than feared."

Some investors are bracing for a potential reversal in September. U.S. lawmakers are scheduled to return to work following an August recess, and could resume talks to end the gridlock on a new coronavirus stimulus package as November election campaigns go into full swing. A failure by Congress to deliver additional relief measures for American consumers and businesses could weigh on market sentiment.

"There's uncertainty about future support," Mr. Dunbar said. "Investors are nervous generally, and keen to see support continue through low interest rates and fiscal policy. Any discussion of that being disrupted can make investors nervous."

Going into the fall, the strength of the economic recovery may also be tested, investors warned, particularly if the number of new coronavirus infections in the U.S. and Europe increases and prompts fresh restrictions on business activity.

"Basically for the U.S. market, we are at a key resistance level," said Nadège Dufossé, head of cross-asset strategy and deputy global head of multiasset allocation at Candriam. "If the market continues to turn more positive, it will benefit value; European and emerging markets' stocks will benefit as investors look beyond the U.S. for returns."

Investors are braced for a surge in volatility stemming from any uncertainty or dispute about the results of the U.S. presidential election, or a sharp deterioration in relations between Beijing and Washington.

China on Friday unveiled new restrictions on artificial-intelligence technology exports that could further complicate the sale of TikTok's U.S. operations, while intensifying the tech battle between the world's two largest economies. Investors appeared to shrug off the implications of the development for the broader market, with optimism about the economic recovery superseding concerns about escalating tensions between the two nations.

But talks aimed at quickly completing a deal between the Chinese parent company of TikTok and suitors for the app's U.S. operations slowed over the weekend following the restrictions, according to people familiar with the matter. Ahead of the opening bell in New York, shares in companies engaged in the talks fell. Microsoft edged down 1.9%, while Walmart dropped 3% and Oracle ticked down 2% in premarket trading.

Overseas, the pan-continental Stoxx Europe 600 wavered between gains and losses. Trading volumes remained low, with markets in the U.K. closed.

"There are only two main themes being played by stock markets. The strong belief in the rebound of all economies -- they are still ignoring the fact that after a V-shaped rebound, the real recovery will have a different shape -- and the strong belief in central banks," said Carsten Brzeski, chief economist for the eurozone at the research division of ING Bank.

"These are completely outweighing the announcements that have the longer-term implications for the global economy," he added.

Among European equities, shares in Suez jumped over 18% on Monday after Veolia Environnement made a cash offer to acquire a 29.9% stake in the French water and waste management company for 2.91 billion euros ($3.45 billion) from Engie. Shares in Veolia and Engie rose almost 6% in Paris.

In Japan, the Nikkei 225 stocks index rose 1.1%, up for the first time in four sessions after Warren Buffett's Berkshire Hathaway said it bought stakes in five of Japan's top corporate names that have big investments in energy. Berkshire took stakes of slightly more than 5% in Mitsubishi Corp., Mitsui & Co., Sumitomo Corp., Itochu Corp. and Marubeni Corp., sending stocks in those companies surging. The five gained between 4.2% and 9.5%.

In bonds, the yield on the benchmark 10-year Treasury ticked up to 0.736%, from 0.727% Friday.

In commodities, Brent crude, the benchmark in international energy markets, rose 0.7% to $46.13 a barrel.

--Frances Yoon contributed to this article.

Write to Anna Isaac at anna.isaac@wsj.com