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The S&P 500 index and the Dow posted their biggest intraday losses in more than five months and the Nasdaq staged its biggest intraday drop in more than four months before clawing back some ground in late morning trading.
All three indexes were headed for their second weekly decline in a row.
"Markets clearly got it wrong and were obviously, to use the British term, 'gobsmacked' by the result," said Aaron Clark, portfolio manager at GW&K Investment Management in Boston. "Investors are shooting first and will ask questions later."
At 11:12 a.m. ET (1512 GMT) the Dow Jones industrial average was down 430.07 points, or 2.39 percent, at 17,581, the S&P 500 was down 54.26 points, or 2.57 percent, at 2,059.06 and the Nasdaq Composite was down 145.99 points, or 2.97 percent, at 4,764.05.
Read more: The Markets are Panicking over Brexit Vote
Investors worried about the outlook for the world economy sought refuge in the dollar and other safe-harbor assets such as gold and U.S. Treasury bonds, while dumping riskier shares. The yield on the U.S. 10-year bond hit its lowest since 2012.
Banks stocks were among the biggest losers. Eight of the 10 major S&P 500 sectors were lower, with the financial index's 3.69 percent leading the decliners. Utilities and telecommunications eked out small gains.
Citigroup was down 8 percent and Morgan Stanley 9 percent, while Bank of America, JPMorgan and Goldman Sachs slumped by between 5 and 6 percent.
U.S. banks have big London operations.
The CBOE VIX volatility index - known as Wall Street's fear gauge - was up 20.35 percent at 20.76 in late morning trading. The index had earlier surged as much as 52.11 percent to 26.24, its highest since February.
"The U.S. equity markets will see selling today but could see a bit of a rebound after the initial knee-jerk reaction as global investors look for somewhere to invest," said Chris Gaffney, President at EverBank World Markets.
By 9 a.m. ET, the number of S&P futures contracts traded had already exceeded their daily average for the past year. Trading in S&P 500 and Nasdaq futures was halted briefly overnight after they fell more than 5 percent, triggering limit thresholds.
Britain's FTSE 100 stock index also recovered much of its early losses and was down 2.2 percent just before the close. Asian stocks also tumbled.
U.S. short-term interest rate futures rose amid speculation the Federal Reserve could cut interest rates to help shield the economy from any global fallout.
Investors have been waiting for the Fed to raise borrowing costs as the economy improves.
The Federal Reserve, which had earlier said a Brexit could have "significant repercussions" on the economic outlook, sought to calm markets on Friday by saying it was ready to provide dollar liquidity.
Amid the turmoil, sterling hit a 31-year low in its biggest intraday percentage fall on record and Prime Minister David Cameron said he would step down by October.
Oil prices, which are sensitive to changes in the economic outlook, dropped about 4 percent, the biggest fall since early February. Exxon and Chevron were down about 1.7 percent.
Among gold miners, Barrick was up 4 percent and Newmont Mining was up 4.75 percent.
Apple, which got more than a fifth of its revenue from Europe last quarter, was down 2.2 percent.
Declining issues outnumbered advancing ones on the NYSE by 2,582 to 424. On the Nasdaq, 2,439 issues fell and 326 advanced.
The S&P 500 index showed 23 new 52-week highs and nine new lows, while the Nasdaq recorded 12 new highs and 85 new lows. (Additional reporting by Noel Randewich; Editing by Alison Williams and Ted Kerr)