TREASURIES-Prices fall before supply, overseas demand stems losses

(Recasts, updates prices)

* Treasuries steady as jobs data meets expectations

* European debt yields fall to record lows

* U.S. debt seen attractive relative to Spanish, Italian bonds

* Treasury to sell $62 bln coupon-bearing debt next week

NEW YORK, June 6 (Reuters) - U.S. Treasuries prices fell on Friday ahead of a $62 billion sale of new coupon-bearing government debt next week, though losses were capped as falling yields on European bonds made U.S. debt relatively attractive. The U.S. government will sell $28 billion in three-year notes on Tuesday, $21 billion in 10-year notes on Wednesday and $13 billion in 30-year bonds on Thursday, new supply that weighed on the market late on Friday. Prices dipped after an earlier rally as overseas investors were drawn to Treasuries by their relatively attractive yields compared with many European bonds. Italian Spanish and Irish bond yields fell to record lows on Friday, a day after the European Central Bank cut all its main rates to record lows, imposed negative interest rates on overnight bank deposits and outlined a new long-term loan program for banks to promote lending to small and mid-sized businesses. "The ECB delivered what the market was expecting in terms of a rate cut and was on the dovish side in terms of easing policies. That is a positive for European bonds and global fixed income. With European bonds rallying, it inevitably drags U.S. rates along with it," said Michael Chang, an interest rate strategist at Credit Suisse in New York. Benchmark 10-year notes were last down 3/32 in price to yield 2.60 percent, after earlier falling as low as 2.53 percent. That compares with 10-year Spanish bond yields at 2.62 percent and Italian bond yields offering 2.73 percent. Irish government bonds paid less than comparable Treasuries for a second day, with 10-year yields dropping to 2.43 percent. Treasuries are likely to remain attractive to many investors as yields on other fixed income assets decline, despite data that show the U.S. economy is gaining traction. "It's going to be hard for the Treasury market to sell off a whole lot, given where peripheral European debt is at the moment," said Dan Mulholland, managing director in Treasuries trading at BNY Mellon in New York. Data on Friday showed that nonfarm payrolls increased by 217,000 last month, returning employment to its pre-recession level and offering confirmation the economy has snapped back from a winter slump. Economists polled by Reuters had expected employment to increase by 218,000 last month. The unemployment rate held steady at a 5-1/2 year low of 6.3 percent even as some Americans who had given up the search for work resumed their hunt. That was because there was an increase in household employment.

(Reporting by Karen Brettell, Editing by W Simon, Dan Grebler and Andrew Hay)