* Euro heads towards low $1.20s on Spain worries * Spanish debt yields near dangerous levels, risk of bailout growing * Italian borrowing costs soar at bond sale By Wanfeng Zhou NEW YORK, May 30 (Reuters) - The euro fell to a near two-year low against the dollar on Wednesday with no relief in sight as Italian borrowing costs soared and concerns mounted over Spain's banking sector. The euro zone common currency looked headed towards the low $1.20s, analysts said. It broke decidedly beneath the psychologically important $1.25 level on Tuesday. Real money and institutional investors stepped up selling on further signs the bloc's debt crisis is spreading to larger economies. Italy's funding costs rose sharply at a bond sale on Wednesday, with 10-year yields topping 6 percent for the first time since January. The Spanish equivalent neared the dangerous 7 percent level that had forced other euro zone countries to seek bailouts. "Uncertainty remains high and headline risk is likely the key driver," said Camilla Sutton, senior currency strategist at Scotia Capital in Toronto. "The fear is that we only have band-aid solutions and we still don't have a medium-term plan for Europe." The euro fell as low as $1.2406 on Reuters data, the lowest since July 1, 2010. It was last at $1.2411, down 0.7 percent on the day. Adding to pressure on the euro were poll results showing Greece's radical leftist SYRIZA party has taken the lead over the pro-bailout conservatives. Greece is holding a national parliamentary election next month that may determine whether the debt-laden country stays in the euro zone. More falls could see the euro test a reported options barrier at $1.2400. Below there it has little chart support until $1.2151, a low hit in late June 2010, and then the 2010 low of $1.1876. It staged the short-lived bounce after the European Commission said the euro zone should move towards a banking union and consider eurobonds and the direct recapitalisation of banks from its permanent bailout fund. But most investors sold into the bounce as "these proposals will take a long time and will entail changes to the treaty," said Geoffrey Yu, currency strategist at UBS. The jump in Italian and Spanish bond yields came a day after Egan-Jones Ratings cut Spain's credit rating, the agency's third downgrade of the country's sovereign rating in less than a month. It cited the country's weak banks. "The euro is in an extremely vulnerable position and downside risks are very strong indeed," said Jane Foley, senior currency strategist at Rabobank. "The Spanish banking crisis has the potential to knock the stuffing out of the euro zone irrespective of the Greek election results." "The issues for Spain are undoubtedly huge and most people are coming round to the idea that it will need to go outside of its borders for assistance. The longer it delays, the more the risk of a bank run." The euro lost 1.4 percent against the safe-haven yen , taking it to a four-and-a-half month low of 97.90 yen. The dollar hit a three-and-a-half month low of 78.88 yen and was last down 0.6 percent at 78.98. The dollar index, which measures its value against a basket of currencies, rise to a 20-month high of 82.834. Technical analysts said a monthly close about the 100-month average in the dollar index around 81.82 may herald a shift in the longer-term trend of the dollar and reverse a multi-year drift lower. The dollar also rose to a 15-month high against the Swiss franc at 0.9679 francs on EBS. The higher-yielding Australian dollar fell 1.2 percent to $0.9725, slipping towards a six-month low at $0.9690, after weaker-than-expected retail sales data underscored the case for interest rate cuts.