* Investors jittery after proposal to tax Cypriot deposits * Euro falls broadly, hits 3-month low vs dollar * Focus on Cyprus parliament vote, peripheral bond yields By Anirban Nag LONDON, March 18 (Reuters) - The euro fell sharply on Monday, hurt by news of a bailout plan for Cyprus that will tax bank deposits and which has raised fears of bank runs elsewhere in the euro zone. Euro zone finance ministers demanded at the weekend that Cypriots pay up to 9.9 percent of their bank deposits in exchange for a 10 billion euro ($13 billion) bailout. The move broke with previous EU protocol that citizens' savings are sacrosanct and led to worried Cypriots emptying cash machines on the island as they rushed to access their funds. The speaker of Cyprus's parliament said lawmakers will vote on the plan on Tuesday, postponing it by a day, as the government works on a plan to soften the blow for small savers. Analysts said any changes to help smaller depositors could limit euro losses, but that overall it would remain vulnerable. The single currency dropped to a three-month low of $1.2882 in Asian trade, before paring losses to last trade down 1 percent on the day at $1.2950. Traders said robust offers to sell were at $1.2980 with most investors likely to use a bounce to initiate fresh bets against the euro. Against the yen, the euro gapped lower in Asian trade and fell 2 percent, briefly breaking through support at 121.68 yen, its 55-day moving average. It was last down 1.3 percent at 122.90 yen cutting some losses on buying by macro funds. "If this tax is levied it will set a precedent. It raises questions over whether other deposits will be safeguarded in other countries," said Jane Foley, senior currency strategist at Rabobank. "Euro zone politicians will be at pains today to manage down the danger of contagion to other (peripheral) markets. The euro will find a little bit of support from that but markets will remain jittery." Yields on bonds of struggling euro zone countries like Spain and Italy rose while those on safe-haven German bunds fell, with investors wary of any fresh signs of contagion from Cyprus. "This decision is crossing the rubicon and has the potential to escalate into something which can drag the euro even lower," said Howard Jones, advisor at money manager RMG Wealth Management. "If I was an international investor, I would be looking to pull money out from European bank deposits and bonds and seek safety in the Swiss franc." Reflecting that nervousness, in the options market one-month euro/dollar implied volatilities jumped to 9.35 percent in early London trade from around 7.7 percent on Friday. Euro/dollar one-month risk reversals which measure the relative demand for options on the euro rising or falling were showing a growing preference for euro weakness. The euro fell 0.5 percent against the Swiss franc to 1.2210 francs and 1 percent against the British pound to 85.55 pence. Both the franc and the pound are bought when risks to the euro zone debt crisis escalate. YEN FIRM The yen was also higher. The highly liquid Japanese currency is considered a safe haven by many investors and sought during times of economic uncertainty and financial market stress. The dollar dropped to as low as 93.45 yen in volatile early trade in Asia, its lowest since March 6 and moving away from a 3-1/2 year peak of 96.71 struck on March 12. It was last down 0.3 percent at 94.90 yen. Some strategists said the yen's strength would be short-lived given bets on more aggressive easing steps from the Bank of Japan, and expectations that euro zone politicians will be able to reassure markets. "It's short-term negative for risk, the euro and dollar/yen but we think it shouldn't last too long ... The broad trend for yen weakness is still intact despite the near-term upside," said Bill Diviney, currency strategist at Barclays in Tokyo. Given the dollar's solid gains against the euro, the U.S. currency rose 0.4 percent against a basket of currencies to 82.61. An improving economy in the United States has underpinned the dollar in recent weeks. Data released on Friday showed U.S. manufacturing was growing, although consumer sentiment in the world's biggest economy faltered to its weakest in over a year and inflation picked up.