In late morning trade, London's benchmark FTSE 100 index shed 1.26 per cent to 6,336.60 points.
Frankfurt's DAX 30 fell 0.13 per cent to 9,460.65 points and the CAC 40 in Paris lost 0.45 per cent to 4,092.86.
European stocks had tumbled Monday on renewed fears of a Greek exit from the eurozone and as the euro struck near nine-year lows against the dollar with the European Central Bank appearing on course to further prop up the single currency.
"It feels like we have moved full circle on the eurozone crisis as markets are yet again dominated by a potential exit from the euro area by Greece," said James Hughes, chief market analyst at Alpari trading group.
"After years of political fighting and billions of euros in bailout money it could be that we are closer to a Greek exit than we have ever been."
The first full week of the new year got off to a traumatic start for dealers as they bet that a January 25 general election in Greece would see a victory for the left-wing Syriza party.
Markets fear the party will roll back austerity measures required under the IMF-EU bailout of the country, which could in turn lead to Greece leaving the eurozone.
In foreign exchange, the euro dropped to $1.1907 from $1.1933 late in New York on Monday. The single currency had begun the week by tumbling to $1.1864 -- the lowest level since March 2006.
Remarks by ECB chief Mario Draghi said that deflation was a threat to the euro zone and that the ECB must be prepared to counter it caused the euro to continue its slide.
The ECB has already used several tools to push inflation in the 19 countries sharing the euro back up to the 2.0 per cent annual rate it regards as healthy, including asset purchases and making cheap loans available to banks.
It is also currently examining the possibility of large-scale purchases of sovereign debt, so-called "quantitative easing" or "QE", to help jump-start the eurozone economy.
With the ECB primed to act, French and German borrowing rates reached new all-time lows on Tuesday amid fears over the prospect of Greece leaving the eurozone.
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