* Front month remains well above January three-month low * Cold weather on tap in long-term outlooks * Nuclear outages still running above normal By Eileen Houlihan NEW YORK, March 4 (Reuters) - U.S. natural gas futures edged higher early on Monday, lifted by forecasts for continued cold weather for most of the United States despite still bloated inventories. As of 9:11 a.m. EST (1411 GMT), front-month April natural gas futures on the New York Mercantile Exchange were at $3.465 per million British thermal units, up 0.9 cent. The nearby contract rose 5 percent last week, its biggest weekly run up in six weeks. It is up about 10 percent over the last two weeks on the lingering cold weather. The contract hit a 6-1/2 week high of $3.645 in late January after touching a more than a three-month low of $3.05 early in the month. Forecaster MDA Weather Services called for below-normal readings across much of the country in its one to five-day outlook, with the cold concentrated from the Midwest to the South. The latest National Weather Service six to 10-day forecast issued on Sunday called for below-normal temperatures for most of the United States, with some above-normal readings on the West Coast and in parts of New England. Nuclear outages totaled about 15,800 megawatts, or 16 percent of U.S. capacity, down from 19,200 MW out a year-ago but up from a five-year average outage rate of about 13,300 MW. ABOVE-AVERAGE STORAGE DRAW U.S. Energy Information Administration data last week showed domestic gas inventories fell the prior week by 171 billion cubic feet to 2.229 trillion cubic feet. The weekly draw came in well above the five-year average drop for that week and storage is now 12 percent below last year's record high levels, but it is also 16 percent above the five-year average level. Withdrawal estimates for this week's storage report range from 120 bcf to 160 bcf versus a 92 bcf draw in the same week in 2012 and a five-year average drop for that week of 107 bcf. Most analysts expect storage to end the heating season at about 2 tcf, or 16 percent above average, but 19 percent below last winter's record-high finish of 2.48 tcf. OUTPUT STARTS TO SLOW? Baker Hughes data on Friday showed the gas-directed drilling rig count fell for the fourth time in five weeks, dropping by eight to 420. The gas drilling rig count is hovering just above the 13-1/2-year low of 413 hit in early November, but production is still high. EIA data last week showed that gross natural gas output in December slipped slightly from November's record high, the first time in four months that production failed to set a new peak. But most analysts pegged the decline to cold weather in the Southwest that likely froze wells and not producers intentionally curbing dry gas flows. The EIA expects marketed gas production in 2013 to hit a record high for the third straight year.