* Bond prices fall on hope for Cyprus deal * Ten-year yields hold in tight range of 1.90 to 1.97 percent * Fed buys $3.68 bln in notes due 2018-2020 By Karen Brettell NEW YORK, March 22 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. "The details from the EU putting the deadline for Monday is helping by giving a timeframe where a decision needs to be made. I think equity markets and risk assets are responding positively to that," said Sean Simko, portfolio manager at SEI Investments in Oaks, Pennsylvania. Russia rebuffed Cypriot entreaties for aid on Friday, leaving leaders scrambling for an alternative deal. Ten-year notes were last down 3/32 in price to yield 1.93 percent, up from 1.92 percent late on Thursday. The notes have traded at yields of between 1.90 and 1.97 percent this week after falling from around 2.06 percent last week. 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 Sean Murphy, a Treasuries trader at Societe Generale in New York. "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," he said. 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 bought $3.68 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.