* New U.S. jobless claims rise to three-month high * Market awaits Friday's U.S. nonfarm payrolls report By Ellen Freilich NEW YORK, April 4 (Reuters) - U.S. Treasury debt prices rose on Thursday, pushing yields to near 3-1/2-month lows, after a jump in new jobless claims suggested key payrolls data due Friday could show the labor market lost some steam in March, an outcome that would favor safe-haven U.S. debt. The number of Americans filing new claims for unemployment benefits rose 28,000 last week to a seasonally adjusted 385,000, the highest level since last November, the U.S. Labor Department said. It was the third straight week of gains in new jobless claims. The benchmark 10-year Treasury note, up 7/32 in price before the jobless claims report, was up 12/32 immediately afterward. Its yield stood at 1.77 percent, after dipping toward a 3-1/2-month low. The 30-year Treasury bond rose 26/32 in price as its yield eased to 3.01 percent. Technical resistance and profit-taking before Friday's nonfarm payrolls report subsequently trimmed some of those gains. The U.S. Labor Department tied some of the volatility in claims to holidays and spring vacations falling in March. Still, jitters about the second-quarter economic outlook were enough to drive a safe-haven bid for Treasuries. "Every year now for three years, we have tended to see Treasury yields rise in the early part of the year and then the economic data seem to slow down as we get into the spring and summer months," said Jim Kochan, chief fixed-income strategist, Wells Fargo Funds Management LLC, Menomonee Falls, Wisconsin. Kochan also said weaker Institute for Supply Management (ISM) indexes for March, particularly for manufacturing, "have some people thinking about a slowing economy. That might not be correct, but that's the sentiment now in the Treasury market." The buying in Treasuries has probably been "international buying more than anything else," he added. "Though we won't have the data for several weeks, typically, when you get these kinds of moves, buying from overseas is a major factor." Whether some of that buying is inspired by the plan to tax uninsured deposits in Cypriot banks as part of a euro zone bailout for the country is "hard to tell," Kochan said. "But certainly, if you were a large depositor in some of the banks in peripheral European countries, you would have to ask yourself whether you should diversify." PAYROLLS DATA AHEAD Below-forecast ADP private payrolls data for March, a non-manufacturing employment component released on Wednesday, had already lowered expectations for the payroll growth investors expect to see in this Friday's employment report. The jump in new jobless claims reported on Thursday reinforced those perceptions, allowing bond prices to rise and yields to ease further. "The big show is (Friday's) employment report for March," said Chris Rupkey, managing director and chief financial economist at Bank of Tokyo-Mitsubishi UFJ in New York. "Economic growth has had a soft patch around this time of year for three straight years and there is evidence that the economy will slow in the second quarter again this year as the European economy is weak and the mandatory spending cuts from Washington start to have a greater impact," he said. That could keep the Fed buying Treasury debt and nudge U.S. government bond yields still lower, strategists said. As part of the Fed's ongoing program of unconventional easing to stimulate lending and economic activity, the Federal Reserve Bank of New York said its open market desk purchased $1.575 billion in Treasury coupons with maturities ranging from Feb. 15, 2036 to Feb. 15, 2043.