The rejection brought the east Mediterranean island, one of the smallest European states, to the brink of a financial meltdown. EU countries said before the vote that they would withhold 10 billion euros ($12.89 billion) in bailout loans unless depositors in Cyprus shared the cost of the rescue.
The euro fell as low as $1.2843, according to Reuters data, its lowest level since Nov. 22, after breaking key support around $1.2870, its 200-day moving average. It was last down 0.5 percent at $1.2894.
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The currency trimmed losses briefly after the Cyprus vote, when the European Central Bank said it was in contact with its IMF and EU partners and remained committed to providing liquidity within existing rules.
The unprecedented plan to impose taxes on citizens' savings in Cyprus, announced over the weekend, sparked fears of a bank run and fueled speculation that larger European countries such as Spain and Italy might do the same should they need financial aid.
Goldman Sachs, in a note to clients, said short positioning in the euro is not stretched yet and that implied volatility remains at levels well below those seen in past periods of stress, suggesting a slide to $1.25 or even lower in the euro/dollar is "entirely possible."
Still, the firm said it remains constructive on the euro in the medium term, saying the Cyprus crisis will provide an entry point for long euro positions.
"Cyprus is very small compared to the overall euro zone with strong financial linkages to non-euro zone countries," Goldman said. "In many respects this make Cyprus a special case with less obvious contagion risks when compared to previous bailouts of euro zone countries."
Some strategists said the market remains insulated by the European Central Bank's as-yet untested promise to buy government bonds in potentially unlimited amounts, if necessary, to help stabilize financial markets.
The euro fell 0.5 percent against the British pound to 85.38 pence after hitting a five-week low. Sterling has been bought as a shelter in times of heightened uncertainty in the euro zone.
Against the Swiss franc, the euro declined 0.4 percent to 1.2211 francs.
Uncertainty about the euro zone benefited the U.S. dollar and Japanese yen, often seen as safe-haven currencies.
The dollar index, which measures the greenback against a basket of currencies, was up 0.3 percent at 82.911, not far from a seven-month peak of 83.166 set on Thursday.
Against the yen, the euro slid 0.6 percent to 122.57. The dollar lost 0.2 percent to 95.07 yen.
Analysts said the yen is vulnerable to any comments from Haruhiko Kuroda, who becomes governor of the Bank of Japan on Wednesday.
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Expectations are high that Kuroda will put in place an aggressive monetary policy to try and lift Japan out of deflation.
Investors are also turning their focus to the end of a two-day U.S. Federal Reserve policy meeting on Wednesday. The Fed looks set to keep buying $85 billion a month in mortgage and Treasury bonds in an effort to encourage investment and bolster a weak economic recovery.