* Milder extended weather outlook keeps buyers cautious * Aggregate inventories remain high, limit price gains * Nuclear outages still running above normal By Joe Silha NEW YORK, March 4 (Reuters) - U.S. natural gas futures ended higher on Monday, with cold weather over most of the United States this week driving the front-month contract near a recent high despite milder forecasts for next week and concerns about sizeable supplies. Fairly cold late-winter weather helped push the front contract up nearly 10 percent in the previous two weeks. Last week's 5 percent gain was the biggest weekly run in six weeks. Strong draws from inventory, utilities using more gas for power generation and significant outages at nuclear plants have also helped prop up prices. Plants burning gas usually make up much of the shut nuclear generation. "Weather is a key factor and we're seeing more persistent cold over a large enough geography, which is giving a lift to prices," said Richard Hastings, macro strategist at Global Hunter Securities, noting chilly weather could stir decent demand into the third week of March. Front-month gas futures on the New York Mercantile Exchange ended up 7.3 cents, or 2.1 percent, at $3.529 per million British thermal units, after trading between $3.408 and $3.539. The nearby contract hit a five-week high of $3.554 last Wednesday. It was the first front-month close above $3.50 in six weeks, and could set the stage for more upside, but most technical traders would like to see a close above the 2013 high of $3.645 posted in late January to turn more bullish. Many traders remain skeptical of the upside, with winter winding down, storage still high and production flowing at or near a record peak. After some cold this week, forecaster MDA Weather Services noted that the six-to-10-day outlook turned warmer for the eastern half of the nation, with some above-normal temperatures stretching from the Midwest to the Northeast. ABOVE-AVERAGE STORAGE DRAW EXPECTED U.S. Energy Information Administration data last week showed domestic gas inventories for the week ended Feb. 22 fell 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 sliced 53 bcf from the surplus versus the five-year average, but traders noted storage is still relatively high at 308 bcf, or 16 percent, above that benchmark. Early withdrawal estimates for Thursday's EIA report range from 120 bcf to 160 bcf. Stocks fell by 92 bcf in the same week in 2012. The five-year average drop for that week is 107 bcf. Most analysts expect storage to end the heating season near 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 last week for the fourth time in five weeks. The gas count is hovering just above the 13-1/2-year low of 413 hit in early November, but production remains high. EIA data on Thursday 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.