The euro fell, touching the lowest level against the U.S. dollar and Japanese yen in more than a decade, while Asian stocks and U.S. futures tumbled after Greece's antiausterity Syriza party was projected to win the country's national elections, fueling fears about the future of the eurozone.

The European currency was down 0.3% against the U.S. dollar to $1.1171, and earlier touched $1.1098, which was the weakest point since Sept. 2003. In Japan, the Nikkei Stock Average was down 0.6% to 17410.91 ahead of the open in Hong Kong where futures for the Hang Seng were down 0.3%. Futures for U.S. stocks were down 0.8%, while futures for West Texas Intermediate crude oil fell 1.5% to under $45 a barrel in Asia trade.

The Syriza party was projected to win 150 seats out of the 300 in Greece's parliament, but it remained unclear whether the party would need to find a coalition partner to form a government. The victory has some analysts concerned that Greece could exit the eurozone, setting a precedent for other countries and shaking up financial markets.

"The signs that are appearing around Greece's elections are throwing renewed doubt on the viability of the euro," says Hiroyuki Fukunaga, chief executive officer at Investrust, an asset manager.

Sam Stovall, U.S. equity strategist at S&P Capital IQ, said investors signaled some concern on Friday, when U.S. stocks sold off after four sessions of gains. "Investors just decided to take gains from Thursday, pocket them because who knows what's going to happen on Sunday," Mr. Stovall said.

But some investors said the election would have a minimal effect on the markets, asserting that any contagion should be short-lived and expressing doubt that Greece would abandon the euro. Some strategists said fourth-quarter corporate earnings would be more important for the stock market than the outcome of Sunday's election in Greece.

Losses in Asia were muted with Australia's market closed for a national holiday. Stocks in New Zealand were up 0.3% while Malaysia was down 0.2%.

The launch of a massive stimulus program by the European Central Bank on Thursday is expected to keep money flows liquid and to encourage investment into risker markets, including stocks in Asia.

Douglas Coté, chief market strategist for Voya Investment Management, said Greece is just a tiny slice of the world economy. "I'm watching it, but there's no panic," Mr. Coté said. "If there is a selloff, it's an opportunity for investors to get in."

Analysts at AXA Investment Management said markets could be volatile in the aftermath of the vote. But they added that even with a Syriza win, Greece's elections are likely to have either a "marginal" effect or "no material impact on the rest of the euro area."

George Rusnak, co-head of fixed income at Wells Fargo Investment Institute, said it would set a better tone for markets if Syriza were required to find a coalition partner. If a partner is needed, "it sets that tone that they have to start negotiating," and could prompt the party's leaders to move away from their most extreme positions, Mr. Rusnak said.

Mr. Rusnak said he has been recommending that investors hold an underweight position in international sovereign bonds from developed countries, noting that Syriza's electoral victory could lead to uncertainty in the short-term. Yields on some short-term European bonds are already negative, meaning bond prices are high, making it difficult to see a major rally on the horizon.

"The key thing is, will they have the majority or not?" Mr. Rusnak said.

Juliet Samuel contributed to this article.

Write to Mike Cherney at mike.cherney@wsj.com

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