In Europe, the Stoxx 600 Index ended the session with a 1.6 percent drop from the previous close, while Greece's ASE Index slumped 4.7 percent.
The UK's FTSE 100 Index fell 1.1 percent, France's CAC 40 Index slid 1.8 percent and Germany's DAX dropped 1.9 percent.
"The market has had a long time to prepare for [a Greek default] and has done what it can with what it sees on the horizon but with situations like this, there is always an unknown factor," Ashwin Bulchandani, head strategist at asset manager MatlinPatterson in New York, told Reuters. "Uncertainty freaks the market out. It makes it very, very nervous."
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European Central Bank President Mario Draghi warned that Greece needs to step up its game.
"We need a strong and comprehensive agreement, and we need this very soon," Draghi told the European Parliament's Committee on Economic and Monetary Affairs in Brussels. "While all actors will now need to go the extra mile, the ball lies squarely in the camp of the Greek government to take the necessary steps."
Meanwhile, the latest US economic data were disappointing.
Industrial production unexpectedly dropped in May, declining 0.2 percent last month, following a 0.5 percent drop in April, according to the Fed. Separately, the New York Fed's Empire State general business conditions index posted a reading of minus 1.98 in June, compared with 3.09 in May.
"Signs of spring remain largely absent in the industrial sector," Tim Quinlan, an economist at Wells Fargo Securities in Charlotte, North Carolina, told Reuters. "The challenges of the stronger dollar and drop in energy prices linger."
The Dow moved lower with slides in shares of United Technologies and those of 3M, down 2.3 percent and 1.3 percent respectively, leading losses.
Bucking the trend, shares of Cigna soared, last trading 12.5 percent higher, after the Wall Street Journal reported Anthem is pursuing a takeover of the company.
Anthem and Cigna have been in discussions for months and within the past 10 days Anthem has made two takeover bids, the last at about US$175 a share, the Wall Street Journal said, citing people familiar with the matter. Anthem's efforts have been rebuffed by Cigna.