* New jobless claims rise to three-month high * Market awaits Friday's U.S. 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 data on new jobless claims suggested key government employment 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 to a seasonally adjusted 385,000, the highest level since November, the U.S. Labor Department said. It was the third straight week of gains in claims. The benchmark 10-year Treasury note, up 7/32 in price before the jobless claims report, was up 12/32 immediately afterwards. Its yield stood at 1.77 percent, after dipping nearer a 3-1/2-month low. The 30-year Treasury bond rose 26/32 as its yield eased to 3.01 percent. Technical resistance and profit-taking before Friday's payrolls report subsequently trimmed some of those gains. The U.S. Labor Department tied some of the volatility in claims to holidays and spring breaks falling in March. Still, there were enough jitters to drive a safe-haven bid for Treasuries. April will be a very important month for jobs. That's when most people expect the impact from the government sequester will hit. "The BOJ move was a healthy surprise," said Robbert Van Batenburg, director of market strategy at Newedge USA LLC in New York, referring to the Bank of Japan's decision to inject $1.4 trillion into the economy in less than two years, a move that sent Japanese bond yields to record lows. "But that was deflated by the (U.S.) jobless claims (jump) and the passive mode of the ECB," he said. The European Central Bank on Thursday held rates steady, taking a wait-and-see stance toward the euro zone recession. "The 10-year Treasury yield is dropping to its lowest level of the year and the euro is falling out of bed. There is a lot of nervousness in the system," Batenburg said. Below-forecast ADP private payrolls data and 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 385,000 new claims don't look good," said Chris Rupkey, managing director and chief financial economist at Bank of Tokyo-Mitsubishi UFJ. "Is it Easter or something more? If it is temporary that is one thing, but you can bet your bottom dollar that nothing good has ever happened to the economy when unemployment claims are rising." Analysts said concerns about second-quarter U.S. growth supported bond prices. "Economic growth has had a soft patch around this time of year for three straight years," Rupkey said. "The big show is tomorrow's employment report for March," he said. "There is evidence that the economy is going to 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." That could keep the Fed buying Treasuries and nudge U.S. Treasury yields still lower, strategists said.