The Dow closed about 260 points lower after earlier falling 337 points. Boeing, McDonald's and IBM had the greatest negative impact as most constituents declined.
The Nasdaq composite closed at its lowest since late February. The index underperformed with a decline of more than 2 percent, weighed by Microsoft and Apple. The iShares Nasdaq Biotechnology ETF (IBB) fell 3 percent.
Investors continued to take a defensive stance, with utilities and telecoms the only advancing S&P sectors. Telecom company Verizon and Johnson & Johnson were the only positive Dow components.
"I think the market's trying to adapt to the uncertainty and volatility," said Marc Chaikin, CEO of Chaikin Analytics.
"It's clearly a shock to the system ... but the ultimate outcome is by no means clear," he said.
In an unprecedented move, Britain surprised markets by voting to leave the European Union late last week. The news raised concerns that other countries might leave the union and that global growth would come under significant pressure, while the actual timeframe of the U.K. departure from the EU remained unclear.
Standard & Poor's announced Monday that it had lowered the United Kingdom's sovereign credit rating from "AAA" to "AA," citing last week's referendum.
The factors behind the decline Monday are "not anything different" from Friday, said Ryan Larson, head of equity trading, U.S., at RBC Global Asset Management (U.S.). "Just a continuation of the concerns regarding the outcome. Unfortunately (it's) not a one-day event, a two-day event, but presents significant uncertainties not only for the U.K. but how the world will be impacted going forward."
"The market was suggesting broader Europe had more to lose than the U.K.," he said. "Today it seems more across the board."
European stocks were sharply lower Monday, with the German DAX off about 3 percent and the STOXX Europe 600 about 4 percent lower.
Asian stocks closed mostly higher, with the Shanghai composite up nearly 1.5 percent and the Nikkei 225 rising about 2.4 percent.
Overnight, Japanese Prime Minister Shinzo Abe said at an emergency meeting between the government and the Bank of Japan that he has instructed Finance Minister Taro Aso to watch currency markets "ever more closely" and take steps if necessary, following the historic Brexit vote, Reuters said.
The People's Bank of China set the yuan's midpoint fix against the dollar at 6.6375, its weakest level since late 2010.
The U.S. dollar index rose more than 2 percent Friday for its best day in more than seven years and the index traded more than 1 percent higher Monday to hit its highest in more than three months. The euro was near $1.102 and the yen around 102.05 yen versus the greenback.
Pound sterling edged below Friday's lows to hit $1.3122, its lowest against the dollar since September 1985. Sterling was last near $1.322.
"I think we're looking at a strong dollar world, almost regardless of what the Fed does," said Thierry Albert Wizman, global interest rates and currencies strategist at Macquarie.
In economic news Monday, the Markit flash services PMI for June came in unchanged from the prior month at 51.3.
Treasury yields held lower, with the 2-year yield around 0.61 percent and the 10-year yield near 1.46 percent. The 30-year yield hit 2.272 percent, its lowest level in more than a year.
The Dow transports closed 3.1 percent lower, with Avis Budget leading nearly all constituents lower.
"It's a lot of follow-through from Friday. There's a lot of uncertainty and panic there. Until the market can get a catalyst to hold onto to get shorts to book gains I expect markets to stay in a downtrend," said John Caruso, senior market strategist at RJO Futures.
Stocks plunged more than 3 percent Friday, with the Dow Jones industrial average and S&P 500 erasing year-to-date gains after the surprise U.K. vote to leave the European Union. Global markets lost a record $2.08 trillion on Friday, according to Howard Silverblatt of S&P Dow Jones Indices. U.S. markets accounted for $830 billion of that loss, he said.