* Prices fall as stocks gain, reducing safety bid * Fed will buy $4.75-5.75 bln in notes due 2017-2018 * Debt ceiling debate starts to gain focus, may boost bonds By Karen Brettell NEW YORK, Jan 11 (Reuters) - U.S. Treasuries prices fell on Friday after the market digested this week's new supply of $66 billion and investors weighed an improving economy against concerns over impending battles over the U.S. debt ceiling. Treasury debt yields have stabilised this week after a dramatic jump in the first three days of the year as investors bet on the prospects of an improving economy and after minutes from the Federal Reserve's December meeting raised the possibility that the central bank may end bond purchases before year-end. Investors are now grappling to find a new range for the debt, with some market participants expecting that an improving economy should send yields higher, though uncertainty remains over raising the U.S. debt ceiling. "You do have a better atmosphere and little more appetite for risk out there, which means Treasuries usually suffer the brunt of that," saud Sean Murphy, a Treasuries trader at Societe Generale in New York. "Overall the mood of the market is a little bit random, the market is still trying to work out what the range should be," he added. Benchmark 10-year notes were last down 6/32 in price to yield 1.93 percent, up from 1.90 percent late on Thursday. The yields are down from a high of 1.98 percent last Friday, and have increased from around 1.70 percent at year-end. Concern over new battles in Washington over how to cut federal spending, reduce the deficit and raise the debt ceiling is likely to add a safety bid that will hold bond yields down even as some investors see the overall direction for yields as still pushing higher. "Overall it does feel like rates would like to go higher," said James Newman, head of Treasuries and agency trading at Keefe, Bruyette and Woods in New York. But "the debt ceiling got in everyone's head, how that will play out." Investors will now be closely watching a speech that Fed Chairman Ben Bernanke is due to give on Monday at the University of Michigan for any further indications of how long the Fed's latest bond purchase program will last. "He's the one pulling the strings and he's the one that wants the QE, so we'll see if he counterbalances some of the hawkish comments," said Newman. The Fed will buy between $4.75 billion and $5.75 billion in notes due from 2017 and 2018 on Friday as part of its latest quantitative easing program, and it has scheduled Treasuries purchases for every day of next week. Treasuries also firmed earlier on Friday after an acceleration in China's consumer inflation rate narrowed the scope for further monetary easing, causing selling pressure in stock markets and supporting safe-haven instruments such as U.S. debt. "We had ... disappointing inflation data out of China and the European equity market has run out of steam this morning - maybe a bit of profit taking - consequently Treasuries have recouped some of their losses." said RIA Capital Markets bond strategist Nick Stamenkovic.