* Bond prices ebb on Greek deal with Cyprus banks * Fed will buy $3-$3.75 bln in notes due 2018-2020 By Karen Brettell NEW YORK, March 22 (Reuters) - U.S. Treasuries prices fell on Friday as investors grew more optimistic Cyprus would reach a deal to avert a meltdown of its banking system. The European Union gave Cyprus until Monday to raise the billions of euros it needs to secure an international bailout or face a collapse of its financial system that could push it out of the euro currency zone. On Friday, however, Cyprus moved a step closer to raising those funds by agreeing to spin off Greek units of debt-ridden Cypriot banks. The Cypriot presidency said the deal had been settled with favorable terms for Cyprus. "I think the market was catching wind that you're going to get some sort of settlement or passage to calm the market," said Sean Murphy, a Treasuries trader at Societe Generale in New York. Ten-year notes fell 7/32 in price to yield 1.94 percent, up from 1.92 percent late on Thursday. The notes have traded at yields of between 1.90 percent and 1.97 percent this week, after falling from around 2.06 percent last week. Investors were still cautious though that much could change over the weekend, and a safety bid may still emerge before the end of the trading day. "Going into the weekend there is the potential to have some risk reduction," said Dan Mulholland, managing director in Treasuries trading at BNY Mellon in New York. Fears that Cyprus' problems could be replicated in other euro zone countries including Spain and Italy have pushed Treasuries yields down this week, despite improving U.S. economic data that had led some market participants to position for yield increases. Traders are now questioning whether further volatility in the euro zone will push benchmark Treasuries again below the 1.90 percent level, or if a resolution to Cyprus' problems will bring attention back to the U.S. economy, and send yields back above 2 percent. "Overall guys aren't really quite sure which way the market is going to break," said Murphy. "There is a good pull for higher rates, and there is a stubborn crowd saying it's the same old story and we're in a low rate environment for a while. It's choppy enough that you're not getting enough on the data front to really convince you to break out one way or another." Investors are scrutinizing data for signs of an improving employment picture, which is seen as key for the Fed to end its ongoing bond purchase program. The Fed will buy between $3 billion and $3.75 billion in debt due 2018 and 2020 on Friday as part of this effort. Most economists expect the Fed to end or taper purchases at the end of the year.