* Front month hits fresh 2013 high * Milder weather on tap in long-term outlooks * Nuclear outages running above normal By Eileen Houlihan NEW YORK, March 11 (Reuters) - U.S. natural gas futures rose on Monday to the highest level of 2013 and their loftiest mark in just over three months, lifted by technical buying for a third straight session despite milder weather forecasts that should dampen late-winter heating demand. The nearby contract is up about 5 percent in the last three sessions and nearly 17 percent from the five-week low of $3.125 per million British thermal units hit in mid-February. Traders said late-winter cold turned the chart picture more supportive and helped prices break through some key technical resistance points. Front-month April natural gas futures on the New York Mercantile Exchange rose 2 cents, or 0.55 percent, to settle at $3.649 per million British thermal units, after trading as high as $3.652, the highest mark for a nearby contract since early December, according to Reuters data. Other months ended higher as well, with the May contract up 1.6 cents at $3.689 and summer months rising about 2 cents each. In the cash market, gas for Tuesday delivery at the NYMEX benchmark Henry Hub in Louisiana rose 7 cents to average $3.64, with late deals firming to 5 cents over the front month, from deals done late Friday at a 1-cent discount. Gas on the Transco pipeline at the New York citygate gained 13 cents to $3.88. But with storage still high, production flowing at or near record levels and the milder weather outlooks, some traders said more upside could be difficult. Forecaster MDA Weather Services called for warmth in the western United States in its one to five-day outlook. The latest National Weather Service's six to 10-day forecast issued on Sunday called for below-normal temperatures in much of the Northeast, the Northwest and in South Florida, but above-normal readings for the rest of the country. Nuclear outages totaled about 16,700 megawatts, or 17 percent of U.S. capacity, down from 19,600 MW out a year ago, but up from a five-year average outage rate of about 15,500 MW. ANOTHER ABOVE-AVERAGE STORAGE DRAW U.S. Energy Information Administration data last week showed domestic gas inventories fell the prior week by 146 billion cubic feet to 2.083 trillion cubic feet. Most traders viewed the decline as bullish for prices, noting it was the third straight week that the draw came in above expectations. A Reuters poll showed traders and analysts had forecast a 134 bcf drop. The draw was also well above the 92 bcf pull seen during the same week last year and the five-year average drop of 107 bcf for that week. Storage is now 361 bcf, or 15 percent, below last year's record highs for this time of year, but it is also 269 bcf, or 15 percent, above the five-year average level. Early withdrawal estimates for this week's inventory report range from 88 bcf to 147 bcf, well above the 66 bcf pulled from storage during the same week in 2012 and the five-year average decline of 74 bcf for that week. A string of strong weekly withdrawals has prompted analysts to sharply lower estimates for end-winter storage, with some expecting inventories to drop to as low as 1.8 tcf, or about 4 percent above average. A Reuters poll in mid-January showed most analysts had expected stocks to finish the heating season at about 2 tcf. So far this winter, nearly 500 bcf more gas has been pulled from storage than last year. RIGS DECLINE; OUTPUT SLOWING LITTLE Baker Hughes data on Friday showed the gas-directed drilling rig count fell 13 to a nearly 14-year low of 407. It was the fifth drop in six weeks, but production has not slowed much, if at all, from the record high posted last year. The EIA expects marketed gas production in 2013 to hit a record high for the third straight year.