* Munis have underperformed global markets * Some deals postponed because of market uncertainty * Muni funds outflows widen By Hilary Russ NEW YORK, June 7 (Reuters) - U.S. municipal bond sales are expected to rise slightly to $8 billion next week, after several deals in the municipal bond market this week struggled to close, were scaled back, or were postponed altogether - a shaky foundation for next week's deals. Investor uncertainty over when the Federal Reserve will begin slowing its massive bond buying program has been weighing on the U.S. debt market since the start of May. Treasury bonds fell again on Friday, adding to losses for a sixth straight week. And the $3.7 trillion municipal bond market underperformed the broader market. The BofA Merrill Lynch US Municipal Security Index < .MERU0A0> was down in the week 0.34 percent, while the broader U.S. Corporate and Government Master Index < .MERB0A0> fell by 0.054 percent. The yield on top-rated 10-year GO muni bonds rose over 40 basis points in May, from 1.66 percent on May 1 to 2.09 percent on May 31, according to Municipal Market Data, a unit of Thomson Reuters. Muni bond prices also fell in secondary trading on Friday, lifting yields by up to 6 basis points - to 12-month highs - and further adding to a negative atmosphere. The 10-year yield on top-rated muni bonds rose 2 basis points to end at 2.13 percent on Friday, while the 30-year yield rose 6 basis points to 3.34 percent, according to MMD's triple-A benchmark scale. On the primary market, the most visible deal reduction this week was a 40 percent cut in a $1.1 billion Massachusetts general obligation bond sale, to about $670 million, because of weakened investor demand. The issuer said it expects to come back to the market to sell the remaining debt once conditions are more favorable. The triple-A rated city of Tempe, Arizona, also struggled to close out a $41 million general obligation refunding sale, particularly in the intermediate part of the curve between 2019 and 2021 maturities with 4 percent coupons, according to Greg David, a municipal fixed-income trader at Wells Capital Management. "This was a great quality bond ... It almost felt like people were getting nervous. They really shouldn't have been," David said. "I think this was just general tone in our market." Tacoma, Washington and Portsmouth, Virginia also had to cheapen deals slightly to clear them, he said. Not everyone is scared away. The current tax-free bond market "is very attractive and offers opportunities for portfolios not seen in a long time," wrote John Mousseau, director of fixed income at Cumberland Advisors, in a note on Friday. "It is the best opportunity in the municipal bond market in the past twelve months." But investor interest as measured by municipal bond funds was waning. Lipper data on Thursday showed that municipal bond funds had net outflows of $1.472 billion in the week ended June 5 from net outflows of $156.86 million the week before. For next week, negotiated sales are expected to total nearly $5.65 billion in 81 issues, compared with a revised $5.4 billion in 84 deals this week. The biggest sale on next week's negotiated calendar is from New Jersey's recently downgraded Rutgers University, which will sell about $877 million of tax-exempt and taxable bonds. Standard & Poor's Ratings Services on Tuesday cut its rating for the state school to AA-minus from AA on increased operational, financial, and credit risk related to its merger with the University of Medicine & Dentistry of New Jersey. Moody's Investors Service also downgraded the university on May 31, to Aa3 from Aa2, because of similar concerns. Rutgers is selling $339.3 million of tax-exempt GO refunding bonds, $399.7 million of new GO bonds and nearly $138 million of taxable GO refunding bonds. Morgan Stanley is the lead manager. The next biggest sale is an $800 million deal from New York City Transitional Finance Authority. Loop Capital Markets is the lead bookrunner for the new money deal. A two-day retail order period begins Monday, with institutional pricing on Wednesday. Illinois is slated to sell $600 million of Build Illinois sales tax revenue junior obligation bonds on Tuesday through Barclays. S&P rated the bonds triple-A. Competitive sales are expected to total nearly $2.37 billion in 170 issues next week. San Francisco, California, tops the competitive calendar, with a planned sale of $232.6 million general obligation bonds. The city of Houston, Texas, will sell $180 million of tax revenue anticipation notes on Wednesday. Proceeds will help finance general operating expenses in fiscal year 2014.