* Front month well below recent 21-month high * Weather expected to moderate over next two weeks * Nuclear power plant outages remain below average By Eileen Houlihan NEW YORK, May 7 (Reuters) - U.S. natural gas futures sank to their lowest level in just over a month on Tuesday, pressured by forecasts calling for moderating temperatures over the next few weeks. Traders said the milder weather forecasts and expectations for another above-average storage injection weighed on prices. Last week's unexpectedly large weekly inventory build led to a 7-percent selloff on Thursday before prices recovered slightly on Friday. Prices remain well under last week's 21-month high hit midweek. A long cold winter put a huge dent in inventories, and lingering cool weather this spring led to a slow start to the injection season. But the onset of milder spring weather starting this week has curbed late-season heating demand before heavy cooling loads kick in. As of 9:12 a.m. EDT (1312 GMT), front-month June natural gas futures on the New York Mercantile Exchange were at $3.985 per mmBtu, down 2.6 cents, after sliding as low as $3.96, the lowest mark since early April. The contract rose to $4.444 last Wednesday, its highest mark since late July 2011. The latest National Weather Service eight to 14-day forecast issued on Monday called for above-normal temperatures for about the western third of the nation and in the Northeast, with below-normal readings in the Southeast and most of Texas and normal readings elsewhere. Nuclear plant outages totaled 18,900 megawatts, or 19 percent of U.S. capacity, up from 18,200 MW out on Monday, but down from 23,500 MW out a year ago and a five-year average outage rate of 21,300 MW. LARGER-THAN-EXPECTED BUILD BUT STOCKS BELOW NORMAL Last week's gas storage report from the U.S. Energy Information Administration showed domestic inventories rose in the prior week by 43 billion cubic feet, above Reuters poll estimates for a 28 bcf build and the year-ago gain of 31 bcf. But inventories started the injection season about three weeks later than expected due to the cold spring. Stocks, at 1.777 trillion cubic feet, are nearly 31 percent below last year and more than 6 percent below the five-year average. Early injection estimates for this week's EIA gas storage report range from 58 bcf to 91 bcf, versus a 30 bcf build in the same week last year and a five-year average rise for that week of 69 bcf. Baker Hughes data last week showed the number of rigs drilling for natural gas in the United States fell by 12 to an 18-year low of 353.