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Stock markets globally fell, but analysts said the declines were less than expected due to expectations that the European Central Bank would act to limit any damage.
The ECB's governing council is due to hold a conference call on Monday afternoon to discuss the provision of emergency funding to Greece's banks. The call was originally to be held at noon. A new bailout deal is needed for Greece to meet a July 20 deadline to repay $3.9 billion of bonds to the ECB.
German Chancellor Angela Merkel and French President Francois Hollande will meet in Paris in the afternoon.
Greece's finance minister quit after the vote and Prime Minister Alexis Tsipras said his government was ready to return immediately to negotiations with creditors in a bid to open shuttered banks.
"I think what we are seeing now is that initial concerns were overblown," said Adam Sarhan, chief executive of Sarhan Capital in New York.
"Cooler heads are prevailing and now Tsipras can go to the creditors and have meaningful conversations. It also helps that the Greek finance minister is out because these negotiations can be very personality driven."
At 9:39 a.m. ET the Dow Jones industrial average was down 127.44 points, or 0.72 percent, at 17,602.67. The S&P 500 was lower 13.98 points, or 0.67 percent, at 2,062.8 and the Nasdaq Composite was down 34.48 points, or 0.69 percent, at 4,974.73.
All 30 Dow components were in the red and nine of the 10 major S&P 500 sectors were lower. The energy index led the declines with a 1.6 percent fall as oil prices fell more than 3 percent after the Greek referendum and on a strengthening dollar.
Data due on Monday is expected to show that the pace of growth in the U.S. services sector slowed in June from the previous month. The Institute for Supply Management's services index data is expected at 10 a.m. ET.
U.S. stocks closed slightly lower on Thursday ahead of the Independence Day weekend and as investors digested mixed jobs data which dampened the economic outlook.
Some analysts say the combination of the Greek crisis and tepid employment data puts off a September rate hike by the Federal Reserve, which has said it will raise rates only when it sees a sustained economic recovery.
Health insurer Humana's shares rose 1.7 percent to $190.23 after bigger rival Aetna said on Friday it would buy the company for about $37 billion. Aetna fell 6 percent at $118.12.
Weight Watchers soared 17.8 percent to $4.82 after the New York Post reported an activist hedge fund was in talks with potential partners about making a takeover offer for the company. The hedge fund and a partner "would like to offer perhaps double" Thursday's closing price, the report said. (http://bit.ly/1gjfCLt)
Declining issues outnumbered advancers on the NYSE by 2,094 to 703. On the Nasdaq, 1,758 issues fell and 722 advanced.
The S&P 500 index showed two new 52-week highs and 26 new lows.
