* The three major stock indices rallied at the end of the day, with the Nasdaq up 0.1%; * Long-term U.S. Treasury yields rebounded slightly; * Tesla rose nearly 5%, as third-quarter delivery data was optimistically viewed.

On Monday, U.S. stocks fluctuated higher, with investors focusing on the latest remarks by Federal Reserve officials and policy prospects, and digesting a series of economic data.

As of the close, the Dow Jones rose 61.29 points, or 0.15%, to 42,124.65 points, the Nasdaq rose 0.14% to 17,974.27 points, and the S&P 500 index rose 0.28% to 5,718.57 points.

The market summary included several regional Fed presidents, including Bostic, Kashkari, and Goolsbee, who spoke on Monday, supporting the central bank's last rate cut and expressing support for further rate cuts for the rest of the year, depending on the data.

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This week's market focus is on the August personal consumption expenditure (PCE) data, which is the Fed's preferred inflation indicator.

Long-term U.S. Treasury yields edged higher, with the closely rate-expectation-linked 2-year U.S. Treasury bond rising 0.3 basis points to 3.57%, and the benchmark 10-year U.S. Treasury bond rising to 3.74%.

Federal funds rate futures indicated that the Fed may cut rates by 75 basis points in the two meetings before the end of the year.

Art Hogan, Chief Market Strategist at B Riley Wealth, said, "This is good enough, although the labor market has weakened, but the economy is still relatively strong."

Hogan added, "In a soft landing scenario, the Fed will be able to address inflation without triggering a recession.

So far, that's still the case."

Regarding the market's narrow fluctuation trend, Sam Stovall, Chief Investment Strategist at CFRA Research in New York, said, "If a soft landing is indeed the most likely outcome, I think investors are still just taking a wait-and-see approach."

In terms of individual stocks, Intel rose 3.3%, with news that investment firm Apollo proposed an investment of up to $5 billion in the chip maker.

Tesla rose 4.9%, as Barclays and Tudor Pickering Holt raised their delivery expectations for the electric vehicle maker in the third quarter.

Other star tech stocks fluctuated, with Amazon rising 1.2%, Meta rising 0.5%, Microsoft falling 0.4%, Apple falling 0.8%, and Google falling 0.9%.

Boeing rose 2.0%, as the company raised contract offers to its approximately 33,000 employees at its main manufacturing center in Seattle on Monday, trying to resolve a strike that has lasted for more than a week.

General Motors fell 1.7%, after Bernstein downgraded the auto maker's stock rating from "outperform" to "in line with the market."

In terms of economic data, U.S. business activity in September continued to expand but slowed down, with the S&P U.S. Services PMI falling to 54.4, the lowest in two months, and the manufacturing PMI falling from 47.9 to 47, hitting a new low in 15 months.

However, the average price of goods and services rose at the fastest pace in six months, which may suggest that inflation will intensify in the coming months.

Chris Williamson, Chief Economist at S&P Global Market, said in a statement, "The initial survey indicators in September suggest that the economy continues to grow at a robust pace, despite the weakening of manufacturing and the huge resistance formed by political uncertainty."

International oil prices weakened, with the market focusing on developments in the Middle East.

The near-month contract of WTI crude oil fell 0.89%, to $70.37 per barrel, and the near-month contract of Brent crude oil fell 0.79%, to $73.90 per barrel.

International gold prices rose slightly, hitting $2680.

The COMEX gold futures contract for delivery in September rose 0.25%, to $2,626.50 per ounce.