In particular, the apparent failure of two pro-bailout ruling parties in Greece to win a majority in the parliament has put the future of its rescue plan in doubt, bringing back into focus questions over the future of the single currency.
In France, Socialist Francois Hollande claimed the presidential seat from Nicolas Sarkozy. The move was widely expected but investors are watching to see how he might push back against a German-led austerity drive.
"The election results at the weekend are not helpful to calming the worries already in the market after disappointing (U.S.) payrolls report on Friday," said Gerhard Schwarz, head of equity strategy at Baader Bank.
"The political uncertainty is increasing and over time the euro zone political landscape looks less predictable."
The euro zone's blue chip index, the Euro STOXX 50 .STOXX50E, opened down 1.1 percent, to 2,224.98, its lowest level since late December.
The euro fell as far as $1.2955, its lowest since January 25 but, with the key UK market closed for a holiday, it edged back to be around $1.3002, at the bottom of its $1.30-$1.35 trading band seen since February.
The fears over the future of Europe's fiscal austerity policies sparked a flight to safety across the world's major markets, lifting German government bond futures to a record high of 142.40 in early trade.
Cash 10-year German yields were 2 basis points lower at 1.56 percent, within a whisker of its record low of 1.549 percent.
World equities as measured by the MSCI world equity index .MIWD00000PUS, fell 0.7 percent to 14-week lows at 319.48 points after Wall Street slumped on Friday when new jobs data showed U.S. hiring slowed for the second month in a row.
The surprisingly weak non-farm payrolls report for April fueled fears of a drop in energy demand helping send Brent crude oil below $113 a barrel, its lowest level since late January.
(Additional reporting by Toni Vorobyova; editing by Anna Willard)
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