NEW YORK — U.S. stocks rallied on Monday to the cusp of their records.

The S&P 500 climbed 1.1% and pulled within 0.3% of its all-time high set earlier this month. The Dow Jones Industrial Average jumped 515 points, or 1.1%, and the Nasdaq composite gained 1.4%.

Apple led the way and rose 3.9% amid optimism about demand for its latest iPhone design. It was the strongest force lifting the S&P 500 and set its own record high.

Cleveland-Cliffs jumped 21.5% after the steel company’s CEO, Lourenco Goncalves, said it would provide details soon about a potential deal with a major global steel producer that could mean bigger profits. He also said his company has potentially found signs of rare earths at sites in Michigan and Minnesota.

Such materials have grabbed the global spotlight after C

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