* Yields increase, 10-year notes back above 2.6 percent * Fed to buy $2.25 bln - $2.75 bln notes due 2021-2023 * March T-bill yields rise as debt ceiling concerns return By Karen Brettell NEW YORK, Feb 4 (Reuters) - U.S. Treasuries yields rose from three-month lows on Tuesday as stocks recovered, reducing the safe-haven demand for Treasuries, and as investors grappled with whether disappointing economic data will extend into Friday's highly anticipated jobs report. A report showing U.S. factory activity was weaker than expected on Monday sent equity markets reeling, and adding to an already dramatic selloff caused by volatility from investors fleeing emerging market assets. A light economic calendar on Tuesday helped stabilize the markets, sending Treasuries yields back higher on reduced demand. "There is a reversal in equities and some other risk assets, which have been fueling the (bond ) rallystocks got a little bounce and Treasuries are following," said Michael Cloherty, head of U.S. rates strategy at RBC Capital Markets in New York. Benchmark 10-year notes were last down 12/32 in price to yield 2.63 percent, up from 2.58 percent late Monday. The yields have fallen from over 3 percent at the beginning of the year. Investors were concerned about whether continuing bad weather could upset Friday's jobs report for January, after harsh weather was blamed for recent economic weakness, including job gains that were well below expectations in December. Employers are expected to have added 185,000 jobs in January, according to the median estimate of 101 economists polled by Reuters. Many investors are taking a more cautious stance than analysts' projections, though only a very pessimistic number is seen as likely to sway the Federal Reserve from continuing to reduce the size of its month bond purchases. The Fed last week cut its monthly bond purchases by $10 billion, to $65 billion. The U.S. central bank is not due to meet again until March, which will give it time to evaluate more data before deciding if it should continue paring bond purchases. The Fed will buy between $2.25 billion and $2.75 billion in notes due 2021 to 2023 on Tuesday as part of its ongoing purchase program. Some dislocations were also seen in the Treasuries bills market on Tuesday as investors again pulled back from certain debt at risk of default if U.S. lawmakers are unable to increase the country's debt ceiling. U.S. Treasury Secretary Jack Lew said on Monday that the government could start defaulting on the government's obligations "very soon" after it runs out of room to borrow under a legal cap on public debt. Washington is due to reinstate a limit on its borrowing at the end of this week and Lew said the administration could use accounting measures to stay under the new cap until the end of February. The government has been reducing its short-term debt issuance heading into next week's deadline, as it has faced restrictions on selling debt that is not needed for immediate expenses. Increased issuance of short-term debt after the deadline may add pressure to the bills that are most at risk of delayed payments. "We're seeing some dislocations in the bill curve with the March bills trading cheap, I think we'll see much more acute dislocations next week," said RBC's Cloherty. The Treasury said on Monday it will auction $8 billion of one-month Treasury bills on Tuesday, $2 billion less than the previous week and the fewest since April 2008. Traders expect those bills to sell at yields of 14 basis points, according to trading in the "when-issued" market. On-the-run one-month Treasuries bills that come due on February 27 yielded 5 basis points on Tuesday, up from half a basis point two weeks ago.