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The gains in U.S. stocks were broad-based, with seven of the 10 major S&P sectors higher. Energy stocks led the gainers with a 0.72% rise as oil prices recovered some losses.
Utilities and telecom service stocks, considered defensive investments, were lower.
"Investors are chasing returns because there is no yield in the bond market," said Andre Bakhos, managing director at Janlyn Capital in Bernardsville, New Jersey.
"They are taking a chance in equities as there is a perception that the U.S. markets are a safe-haven on a relative international basis."
Yields on 10-year U.S. Treasury notes rose, but remained close to the record low hit in the aftermath of Britain's vote to leave the European Union.
The electoral success of Japanese Prime Minister Shinzo Abe and the emergence of Theresa May as the sole British PM candidate quelled some of the political uncertainty that has roiled markets in the past few weeks.
The S&P 500 touched a record intraday high of 2139.34 points, topping a high of 2134.72 it hit in May 2015. At 10:10 a.m. ET (1410 GMT), it was up 7.61 points, or 0.36%, at 2,137.51.
The Dow Jones Industrial Average was up 87.69 points, or 0.48%, at a more than 13-month high of 18,234.43, while the Nasdaq Composite index was up 33.82 points, or 0.68%, at 4,990.57.
Much of how the indexes perform over the next few weeks will depend of the quality of second-quarter corporate earnings, which kick off with Alcoa reporting results after markets close on Monday.
"We have entered the gateway to earnings and that could change everything. If they start to underwhelm investors, that could certainly derail the euphoria," Bakhos said.
Earnings of S&P 500 components are expected to fall 4.8%, compared with the year-earlier quarter, according to Thomson Reuters data. First-quarter earnings had fallen 5%.
Investors will also watch out for comments from company executives, especially those of big banks later this week, on the impact of Britain's vote to leave the European Union.
While recent data has pointed to a recovery in the U.S. economy, the Federal Reserve is expected to remain cautious on raising interest rates as it gauges the fallout of the Brexit vote.
Traders have priced in a mere 27% chance a rate hike in December, according to CME Group's FedWatch tool. The Fed next meets on July 26-27.
Shares of Apple rose 0.7% to $97.36 and provided the biggest boost to the S&P and the Nasdaq.
Electric car maker Tesla rose 3.7% to $224.99 after CEO Elon Musk on Sunday tweeted his intention to soon publish part two of his "top secret Tesla masterplan".
Twitter fell 2.5% to $17.64 after SunTrust Robinson lowered its rating to "neutral" from "buy".
Advancing issues outnumbered decliners on the NYSE by 2,105 to 687. On the Nasdaq, 1,852 issues rose and 706 fell.
The S&P 500 index showed 58 new 52-week highs and no new lows, while the Nasdaq recorded 112 new highs and three new lows.