Traders at the Frankfurt Stock Exchange where the DAX 30 index shed 1.29 percent to 11,712.62 points
Anxiety over Greece's new anti-austerity leadership and unexpectedly poor US performance data weighed down European stock markets on Tuesday, analysts said.
Frankfurt's DAX 30 index sank 1.57 percent to close at 10,628.58 points, while in Paris the CAC 40 shed 1.09 percent to 4,624.21 points.
London's benchmark FTSE 100 index of top companies edged down 0.6 percent to end the day at 6,811.61 points, as investors also digested data showing Britain's economic growth slowed to 0.5 percent in the fourth quarter of 2014.
The Athens stock market plunged more than six percent before recovering slightly at the close as investors fretted over whether the new radical left government will renege on Greece's international bailout.
The main Athex index had tumbled 3.2 percent the previous day on news that anti-austerity party Syriza had won the Greek election.
"Gravity took hold... after several days of huge gains inspired by the beginning of a quantitative easing program by the European Central Bank," said Jasper Lawler, an analyst at CMC Markets UK.
"Banking stocks led the declines in a delayed reaction to the risk posed by their Greek counterparts on a possible Grexit," he added, referring to the spectre of Greece being forced to leave the eurozone.
Shares in Germany's Deutsche Bank plunged 3.39 percent, while in France Societe Generale lost 2.3 percent and Britain's RBS was off 1.77 percent.
New Greek Prime Minister Alexis Tsipras unveiled his anti-austerity coalition administration, bringing together his radical left-wing party with a small party on the nationalist right, after a stunning election win that sent shockwaves through Europe.
The appointment of radical left-wing economist Yanis Varoufakis as his finance minister was seen as a signal that the new government will take a hard line in haggling over Greece's 240 billion euro ($269 billion) EU-IMF package.
Tsipras declared Sunday that Greece is "leaving behind disastrous austerity" and the so-called troika of creditors "is finished", in reference to the country's international lenders the European Union, the International Monetary Fund and the European Central Bank.
Syriza are the first anti-austerity party to govern in Europe, but they fell two seats short of a 151-seat majority in parliament and were thus forced to forge the coalition with the small nationalist Independent Greeks (ANEL) party.
- 'Unforeseen development' -
In New York, the Dow slumped more than two percent in mid-morning trade following a raft of mostly weak earnings reports from big companies and a surprising drop in durable goods orders.
Near 1600 GMT, the Dow Jones Industrial Average stood at 17,320.29, down 2.03 percent.
The broad-based S&P 500 sank 1.60 percent to 2,024.24, while the tech-rich Nasdaq Composite Index plummeted 2.09 percent to 4,671.83.
New orders for long-lasting industrial goods fell 3.4 percent in December, signalling some persistent weakness in the manufacturing sector, according to Commerce Department data.
"A Greek election was supposed to cause market ructions but as usual it was an entirely unforeseen development -- namely a slump in US economic performance -- that has created greater excitement," said Chris Beauchamp, a market analyst with IG.
In foreign exchange activity on Tuesday, the European single currency bounced to $1.1368, having hit Monday an 11-year low of $1.1098 on fears that Greece could leave the eurozone.
Most Asian stock markets climbed Tuesday on hopes Greece's new government will be able to negotiate a bailout deal with the EU and IMF that will prevent it from leaving the eurozone.