* Ten-year note yields increase, back above 2.60 percent * Fed buys $2.66 billion in notes due 2022-23 * Fed to buy TIPS, Treasuries in two operations on Wednesday * U.S. sells 1-month bills at highest yields since October By Karen Brettell NEW YORK, Feb 4 (Reuters) - Treasuries yields rose from three-month lows on Tuesday as pressure on stocks and emerging market assets eased, reducing safe-haven demand for U.S. government debt. Treasuries have benefited in the past week from a flight-to-safety bid as worries over high deficits in emerging economies as well as the impact the U.S. Federal Reserve's pullback in stimulus would have on investment there, caused investors to flee those higher-risk assets. Some of those jitters appeared to ease on Tuesday, helping stocks gain and reducing some demand for U.S. government debt. "The whole catalyst for the (bond) rally in the last week or so has been 'risk off' in their markets, concern over emerging markets and equities in general. As you see them rallying back today its taking some of the flight-to-quality bid out of our market," said Rick Klingman, a Treasuries trader at Societe Generale in New York. U.S. benchmark 10-year Treasury 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 start of the year, but have struggled to stay below the 2.60 percent level where there is technical resistance. Thirty-year bonds fell 1-5/32 in price to yield 3.60 percent, up from 3.54 percent on Monday. Some concerns over economic strength also hit the U.S. on Monday after a report showing U.S. factory activity was weaker than expected sent equity markets reeling and benchmark 10-year note yields to their lowest levels since the beginning of November. Investors are now grappling with whether disappointing economic data will extend into Friday's highly anticipated U.S. jobs report for January. Many traders and analysts see it as unlikely that the jobs data will sway the Fed from the course of reducing its asset purchases unless it is much weaker than currently expected. "I think we would need a dramatic weakening in labor conditions to put (tapering) on hold," said Michael Cloherty, head of U.S. rates strategy at RBC Capital Markets in New York. Employers are expected to have added 185,000 jobs in January, according to the median estimate of 101 economists polled by Reuters. The Fed last week cut its monthly bond purchases by $10 billion, to $65 billion. Richmond Federal Reserve President Jeffrey Lacker said on Tuesday that it would be hard to make the case for a pause in tapering. Chicago Federal Reserve Bank President Charles Evans also said that only a sharp economic downturn or unexpected rise in inflation could force the Fed to pause or speed up the pace at which it is cutting the program. The Fed bought $2.66 billion in notes due 2022 and 2023 on Tuesday as part of its ongoing purchase program. It will conduct two operations on Wednesday, including purchasing between $0.85 billion and $1.15 billion in Treasuries Inflation-Protected Securities (TIPS) due from 2018 to 2043, and between $2.5 billion and $3.0 billion in Treasury notes due 2019 to 2021. Some dislocations were also seen in the Treasury 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 U.S. sold $8 billion in one-month Treasury bills on Tuesday at the highest interest rate since mid-October, $2 billion less than the previous week's auction and the fewest notes since April 2008. The Treasury said it would pay dealers and investors 0.13 percent on the bills due on March 6. This was the highest interest rate it paid on one-month bills since the 0.24 percent on $20 billion in one-month T-bills auctioned on Oct. 16. On-the-run one-month Treasuries bills that come due on Feb. 27 yielded 4 basis points on Tuesday, up from half a basis point two weeks ago.