Following a meeting with leading members of the Greece government on Monday, ostensibly to discuss the failure of talks with lenders at the weekend, Greek Prime Minister Alexis Tsipras blamed creditors for the deadlock – a claim rebuffed in Europe.
Michael Fuchs, vice chairman of Germany's CDU/CSU - the ruling conservative coalition, led by German Chancellor Angela Merkel -- told CNBC Tuesday that Greece needed to decide whether to stay in or get out of the euro zone.
Greek stocks remained under pressure, slipping to close around 4.8 percent lower.
Elsewhere on Tuesday, investors were watching for signs of a looming interest rate hike from the Fed as a meeting of its monetary policy committee got under way. The central bank is expected to adjust its economic and interest rate forecasts and possibly tweak its statement, while continuing to emphasize that rate hikes are dependent on economic data.
In other news, the U.S. and Europe's relationship with Russia could deteriorate further on the military front. Russian President Vladimir Putin announced that Russia would add more than 40 ballistic missiles to its nuclear arsenal this year.
Read MoreRussia warns of 'new military confrontation' in Europe