TREASURIES-Prices ease as jobless data boosts risk appetite

* US weekly jobless claims unexpectedly fall

* Stocks strength undermines demand for lower-risk US debt

* Treasury to sell $13 bln of 30-year bonds

NEW YORK, March 14 (Reuters) - U.S. Treasuries prices eased for a second day on Thursday after data showing fewer-than-expected weekly U.S. jobless claims suggested solid improvement in the labor market, while higher stocks undermined the appeal of lower-risk government debt. Investors were also pushing to undermine Treasuries prices heading into the Thursday afternoon auction of $13 billion of reopened 30-year bonds. Treasury debt yields began the session trading higher in tandem with Spanish bond yields after an auction of longer-term Spanish debt was met with healthy demand. Price losses were extended after data showing the number of Americans filing new claims for unemployment benefits unexpectedly fell last week, marking the third straight week of declines. "Overall there is no one specific reason for the back-up but the 'risk-on' tone, continued press higher in equities and looming supply are all playing a role," said Justin Lederer, Treasury strategist at Cantor Fitzgerald in New York, adding, "better than expected (jobless) claims ... resulted in fresh intra-day lows across the curve." Benchmark 10-year Treasury notes were trading with a yield of 2.05 percent, up from a high yield of 2.03 percent in an auction of reopened 10-year notes on Wednesday. Thirty-year bonds were trading 15/32 lower in price to yield 3.24 percent, from 3.22 percent late Wednesday. When it comes to the economy, "everything is just less bad," said Ellis Phifer, senior market analyst at Raymond James in Memphis, Tennessee. He expects the 10-year note yield to touch 2.15 percent if the stock market continues its winning streak. The Treasury will auction $13 billion of reopened 30-year bonds on Thursday, following solid demand in the sales of $21 billion of reopened 10-year notes on Wednesday and $32 billion of three-year notes on Tuesday. In the when-issued market, considered a proxy for where the bonds will price at auction, 30-year bonds were also yielding about 3.24 percent. The Treasuries market on Thursday largely shrugged off data showing U.S. producer prices in February rose by the most in five months as gasoline prices spiked. Overall, the report showed little sign of a broader increase in inflation pressures. The Labor Department said its seasonally adjusted producer price index increased 0.7 percent last month after advancing 0.2 percent in January.