The Dow moved higher as gains in shares of Merck and those of Home Depot, up 2.1 percent and 1.6 percent recently, outweighed declines in shares of DuPont and those of Verizon, recently 2.1 percent and 0.8 percent weaker respectively.
"The selloff last week was an over-reaction and the attempted rally was too fast and furious," Art Hogan, chief market strategist at Wunderlich Equity Capital Markets, told Reuters. "I think the compression of time and speed of the markets causes the pendulum to swing too far on every move we make."
Meanwhile, Goldman Sachs expects the S&P 500 will fall as much as 10 percent before it will recover to 2,100 by the end of the year.
"Although investors appear complacent in the wake of Brexit, a maturing economic cycle with elevated valuations, decelerating buybacks, and growing political uncertainty provide the basis for potential market weakness in the second half," Goldman Sachs chief US equity strategist David Kostin and his team wrote, according to Bloomberg.
"However, above-trend US GDP growth, a cautious Fed, and an earnings recovery will return the S&P 500 to 2,100 by year-end, extending the flat market of the past two years."
Indeed the latest data on the US economy were better than anticipated. An Institute for Supply Management report showed its non-manufacturing index rose to 56.5 last month, the highest since November, and up from 52.9 in May.
"The economy continues to move forward at a good clip and is in a strong position to weather the uncertainty and market volatility after the Brexit vote," Chris Rupkey, chief economist at MUFG Union Bank in New York, told Reuters. "We still don't think Brexit means that much for this economy."
Europe's Stoxx 600 Index finished the session with a slide of 1.7 percent from the previous close, as bank shares weakened. The UK's FTSE 100 index dropped 1.3 percent, while Germany's DAX index dropped 1.7 percent and France's CAC 40 index slid 1.9 percent.
Shares of Deutsche Bank, Credit Suisse Group, Banco Popular Espanol and Italy's Banco Popolare Societa Cooperativa all touched fresh record lows, according to Bloomberg.