The Dow dropped 0.3 percent in the first minutes of trade, continuing last week's decline.
"Greece indicated over the weekend that it will not meet the deficit targets for 2011 and 2012 it set just a short time ago on account of its recession being deeper than previously thought," noted Patrick O'Hare of Briefing.com.
"This news did not sit well on the continent or in Asia. Major averages in those regions, which were drafting off Wall Street's poor finish on Friday, have fallen between one percent and four percent today."
"Things are looking relatively better on Wall Street this morning, but that isn't to say they are looking good."
Traders were looking to two events that could provide some upward momentum for stocks.
The 17 countries that share the debt-challenged euro currency will meet in Luxembourg from 1500 GMT to review the situation. Markets will also hope for a lift from US manufacturing data set to be released at 1400 GMT.
"(It) should play a large role in determining the market's direction today," O'Hare said of the manufacturing index.
The Dow Jones Industrial Average opened down 36.10 points (0.33 percent) at 10,877.28.
The S&P 500 dropped 3.87 (0.34 percent) to 1,127.55, and the tech-heavy Nasdaq fell 12.78 points (0.53 percent) to 2,402.62.
Copyright AFP (Agence France-Presse), 2011