Greece's Prime Minister Antonis Samaras failed to get enough support for his nominee, Stavros Dimas, and will now have to call a national election for late January or early February, which polls suggest would catapault the left-wing Syriza party to power.
European markets reflected uncertainty about Greece's future in the euro zone under a possible Syriza government.
Stocks in Athens plunged more than 11 percent at one point and yields on the country's government bonds spiked sharply, while Italian and Spanish markets also took heavy hits as investors instead made a dash for ultra-safe German debt.
"A Greek accident has become a potent risk. But mostly for Greece itself," said Holger Schmieding at Berenberg Bank in London.
"Of course, the tail risk of Grexit poses questions for Europe. But if that tail risk were to materialise, we see no significant probability that any other country would want to follow."
Away from Athens, trading was thin with many traders still off after the Christmas break.
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Futures markets pointed to a 0.1-0.2 percent dip from record highs for Wall Street when trading resumes, while the Russian rouble's recent rebound ran out of steam as it dropped as much as 6 percent.
Asian stocks rose with MSCI's broadest index of Asia-Pacific shares outside Japan rising 1 percent, helped by gains of 1.5 and 1.8 percent respectively in Australian and Hong Kong shares.
Tokyo's Nikkei bucked the trend and slid 1 percent as reports of a suspected Ebola case in Japan spooked a market still on track for about an 8 percent gain this year.
In Malaysia, shares in AirAsia posted their biggest one-day drop in more than three years after one of its aircraft went missing on its way to Singapore from Indonesia.
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After the Greek vote, yields on 10-year bonds rose above 9 percent, up more than 50 basis points on the day, forcing up yields on other low-rated euro zone government debt.
Former European Commissioner Dimas, the ruling coalition's presidential candidate, had needed 180 votes but got just 168 as he had in the previous round.
The euro, perhaps surprisingly, was little moved by the result but at $1.2190, it was not far from the $1.2165, post-August 2012 low hit the previous week.
The dollar, meanwhile, stood firm at 120.200 yen, remaining in sight of a 7-1/2 year high of 121.86 hit earlier in the month, but lacking enough momentum to challenge that peak. This year, the greenback has risen roughly 15 percent against the yen.
On the 2015 outlook for risk assets, investors will be concerned about whether the strength of the U.S. economy will be able to offset signs of slowdown in powerhouse China and the euro zone.
There is also uncertainty about the impact of the 45 percent drop in oil prices over the last six months on many of the larger producers that depend on oil revenues.
After two days of falls, oil prices rose as escalating clashes in Libya stoked worries about supply.[O/R]
A fire caused by fighting at a main export terminal has destroyed 800,000 barrels of crude - more than two days of Libya's output - officials said, amid clashes between factions battling for control of the country.
"Libya, and all the other problems, warrants some kind of risk premium," said Jonathan Barratt, chief investment officer at Sydney's Ayers Alliance.