* Front month remains well below recent 21-month high * Weather mixed over the nation, cool early in week in East * Nuclear power plant outages still above normal By Eileen Houlihan NEW YORK, May 14 (Reuters) - U.S. natural gas futures rose more than 1 percent early on Tuesday, lifted by continued cool weather early this week in the Northeast that could again slow down inventory builds. In addition, above-average nuclear power plant outages also helped firm near-term demand. But traders expect the cooldown in the East to be the last stretch of heating demand after a long, cold winter put a huge dent in inventories and a cool spring led to a slow start to the injection season. But forecasts for milder weather later in the month should curb any lingering heating loads before heavy cooling demand kicks in. As of 9:16 a.m. EDT (1316 GMT), front-month June natural gas futures on the New York Mercantile Exchange were at $3.984 per million British thermal units, up 5.9 cents, or more than 1 percent. The contract hit a one-month low of $3.883 last week after climbing to a 21-month high of $4.444 on May 1. The latest National Weather Service six to 10-day forecast issued on Monday called for above-normal temperatures in the Northeast and Southwest and below-normal readings along the Gulf Coast stretching into the Plains as well as in the Northwest. Nuclear plant outages totaled 20,100 megawatts, or 20 percent of U.S. capacity, down from 20,400 MW out on Monday, but up from 16,800 MW out a year ago and a five-year average outage rate of 17,900 MW. ANOTHER LARGE BUILD, BUT STOCKS BELOW NORMAL Last week's gas storage report from the U.S. Energy Information Administration showed domestic inventories rose the prior week by 88 billion cubic feet, above Reuters poll estimates for an 83-bcf build, a year-ago gain of 30 bcf, and the five-year average build of 69 bcf for that week. But inventories, which started the injection season about three weeks later than expected due to the cold spring, are at 1.865 trillion cubic feet, more than 28 percent below last year and 5 percent below the five-year average. Early injection estimates for this week's EIA report range from 88 bcf to 106 bcf, versus a 56-bcf build in the same week last year and a five-year average rise for that week of 83 bcf. Baker Hughes' data last week showed the number of rigs drilling for natural gas in the United States slid by four to an 18-year low of 350.