The euro fell against the dollar and the pound on Monday following weekend election results.
Poor performances by pro-bailout parties in Greece and the victory of Francois Hollande in France, who wants to focus more on growth, have cast doubt on European austerity plans.
The euro fell as low as $1.295, its lowest since January, and dropped to three-year lows against the pound.
European stock markets fell, with Germany's Dax trading 1.2% lower.
By late-morning, the Cac 40 in Paris was trading down 0.9%. Athens shares were trading down by 8.3%. London markets are closed for a public holiday.
European markets had also fallen sharply on Friday following the release of US unemployment figures.
The interest rates on some government debt has also gone up, indicating a fall in investor confidence. The yields in the secondary markets for Greek 10-year bonds has gone up from 20% to 22.2%.
The yield on French 10-year bonds has also risen from 2.81% to 2.84%.
Asian markets also fell, with the Nikkei in Tokyo dropping 2.8%.
In Greece, the socialist Pasok party saw an unexpectedly poor result, while Syriza, which has opposed austerity measures, had a strong performance.
The result has cast doubt on whether the country's policies that currently include spending cuts, tax increases and state job losses, can continue.
"The Greek side of things is a ticking time bomb," Justin Harper of IG Markets told the BBC.
"The fear now is that all the hard work that had gone into getting the second bailout package may start to unravel and we can expect some real pressure on stock markets in the coming days."
BBC Europe editor Gavin Hewitt says Greece faces political turmoil.
"Pro-austerity parties were punished at the polls. The country will struggle to form a coalition that has the support in parliament for new spending cuts that are a pre-condition for receiving funds from a bailout," he said.
"There will be fresh doubts as to whether Greece can remain in the euro. The new political reality in Europe is that voters appear no longer willing to accept spending cuts, low growth and unemployment."
Greece is perhaps the result that could be more disruptive of the euro's future.
Without international support, the government could not pay its bills, and that support has come with conditions - painful steps to reduce its budget deficit.
The question now is which parties will form a new coalition government; and will it repudiate the austerity policies?
If it does then the rest of the eurozone and the International Monetary Fund will have to decide if the bailout will continue.
If not, Greece could conceivably end up leaving the euro. We are still a long way from that, and it is important not to underestimate European leaders' desire to hold the eurozone together.
In France, Francois Hollande wants to put more emphasis on economic growth.
A few weeks ago that looked like it might upset Europe's laboriously agreed pact, which is intended to convince the markets that government finances won't be allowed to get out of hand again.
But there are signs of a wider shift of emphasis in the eurozone - more on growth, less on austerity. Mr Hollande can probably be accommodated.
While the French result was expected, there is still concern about whether Mr Hollande will be able to work as closely with German Chancellor Angela Merkel as his predecessor Nicolas Sarkozy did.
The two were the driving force behind the eurozone's fiscal compact.
Mr Hollande stood on a platform of promoting growth rather than concentrating on austerity.
"The Merkel-Hollande initiative will never materialise due to Hollande and Merkel being polar opposites with no chance to agree on anything," Jeff Sica, president of Sica Wealth Management.
The ratings agency Standard and Poor's, which downgraded France from its triple-A rating in January said it the election result would have no immediate impact on its credit status.
"We will analyse the policy choices of France's president elect and the new government, taking into account the outcome of the parliamentary elections in June," the agency said.
"The chances are that the next move is going to be down. The chances are it's going to be slightly earlier than it would have been otherwise, but the agencies themselves will have a measured response," said Georg Grodski, head of credit research at Legal and General.
"There is still hope that Mr Hollande will tone down some of his rhetoric and accept that you can't fix an economic problem by living on other people's money."
Source BBC News