The major averages fell back into negative territory after briefly trading in the black.
The Nasdaq traded about 0.7 percent lower as the iShares Nasdaq Biotechnology ETF (IBB) struggled to hold onto a brief jump of more than 1 percent.
"I think the markets are trading (off the idea that) it's just the next round of negotiations," said Alan Skrainka, chief investment officer at Cornerstone Wealth Management. "It seems to me the markets are taking this in stride because they believe the events in Greece will not have knock-on effects for Europe, or the U.S. for that matter."
"There's a lot of cash on the sidelines," he said. "Many investors who have been left out of the bull market see a little correction (and are) taking advantage of this dip."
The Dow Jones industrial average closed about 46 points lower, falling below its 200-day moving average. However, the index did recover from a 150-point decline soon after the market open.
The Dow transports gave up early gains to close about half a percent lower, remaining below its 200-day moving average.
Futures recovered in morning trade, with the Dow futures about 160 points lower after falling more than 200 points Sunday evening.
"This is a 'it could have been worse' scenario," said Art Hogan, chief market strategist at Wunderlich Securities. "But the question is what's next. To me it's very much trying to ascertain what next steps are. We may get some good news over the next 48 hours."
In a Sunday referendum, nearly two-thirds of Greeks voted "no," rejecting a proposal from international creditors that would have required more austerity reforms for debt relief.
Lead bailout negotiator Euclid Tsakalotos was appointed Greece's next finance minister after Yanis Varoufakis resigned on Monday.
"Investors should brace for volatility with probability of a snapback based on ECB and Eurogroup action over the next few days," said Doug Cote, chief market strategist at Voya Investment Management. "This is not a sell signal."
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Bond yields held lower, with the 10-year yield near 2.30 percent and the 2-year yield around 0.60 percent.
The U.S. dollar trimmed gains to trade flat, with the euro near $1.106.
The European Central Bank said in a Dow Jones report that it will maintain emergency liquidity assistance for Greek banks. Euro zone leaders will meet at an emergency summit on Greece Tuesday.
"Germany is still taking a hard line against Greece and that may have caused the latest selloff," said Peter Cardillo, chief market economist at Rockwell Global Capital.
"The key is not so much when talks resume (but) if the ECB increases loans," he said.
German Chancellor Angela Merkel said after a meeting with French President Francois Hollande that they respect the vote of the Greeks and the door for talks with the country remains open, Reuters reported.
Last week, Greece became the first developed nation to default on a major loan from the International Monetary Fund.
The nation's banks and stock exchange have been closed since last Monday as the government seeks to prevent a massive outflow of cash. The Greek Bank Association head said in a Reuters report that banks will remain closed on Tuesday and Wednesday, while maintaining the daily withdrawal limit of 60 euros.
The Greek rejection of the creditors' proposals weighed heavily overseas. Asian stocks outside of China fell, with the Nikkei closing about 2 percent lower and the Hang Seng down nearly 3.2 percent. European stocks closed lower, with the DAX off 1.5 percent. Italy's FTSEMIB closed in correction territory, joining France's CAC 40 and the Spain IBEX 35.
Shanghai bucked the trend in another volatile day of trade, closing up 2.42 percent but still in bear market territory.
U.S. economic data out Monday included the Institute for Supply Management's June service sector survey, which hit 56.0 in June, versus the 56.2 estimate.
Markit's services PMI for June showed a final read of 54.8.
After last Thursday's soft jobs report, investors will weigh any subsequent data points to see if support is strong enough for a September rate hike.