* Front month ties 2013 high then slips * 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 edged lower early Monday, pressured by milder weather forecasts that should curb any late-winter heating demand. As of 9:33 a.m. EDT (1333 GMT), front-month April natural gas futures on the New York Mercantile Exchange were at $3.611 per million British thermal units, down 1.8 cents, or less than 1 percent. The nearby contract rose as high as $3.645 in electronic trade, a more than six-week spot chart high and tying the highest mark so far for 2013. Cold weather had helped push the front contract up about 15 percent in the past three weeks, turning the chart picture more supportive as prices broke through some key technical resistance points. But with storage still high, production flowing at or near record levels and the milder weather outlooks, 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 six to 10-day forecast issued on Sunday called for below-normal temperatures in much of the Northeast and the Northwest and in South Florida, but above-normal readings for the remainder 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 on Wednesday 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 for that week of 107 bcf. 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 139 bcf, well above the 66 bcf pulled from storage during the same week in 2012 and the five-year average decline for that week of 74 bcf. A string of strong weekly withdrawals has prompted analysts sharply to 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 at this time. 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.