* Front futures rebound for 2nd day after 3 weekly declines * Moderating weather seen slowing demand for next 2 weeks * Coming up: Reuters natgas storage poll, EEI power output Wednesday By Joe Silha NEW YORK, May 14 (Reuters) - Front-month U.S. natural gas futures ended higher on Tuesday for a second straight day, backed by cool Northeast weather early this week that has lifted demand despite milder forecasts for later this week and next week. Gas prices slid more than 11 percent in the previous three weeks as moderating weather curbed heating loads. But prices have gained 3 percent so far this week as temperatures cooled. Chart traders agreed the front contract was oversold after a three-week slide and due for a bounce, particularly with prices testing technical support in the $3.90 per mmBtu area several times over the last week but unable to settle below it. "I thought we would be working a little lower this week, but technical support has been holding, and it's still a little chilly up north," said Tom Saal, senior vice president at INTL FCStone in Miami. Front-month gas futures on the New York Mercantile Exchange ended up 10 cents, or 2.5 percent, at $4.025 per million British thermal units after trading between $3.923 and $4.028. The front contract hit a 21-month high of $4.444 two weeks ago, then posted a five-week low of $3.883 last week. Traders said the sharp slide in the June-January carry, which has dropped 7 cents, or nearly 16 percent in the last week to 37.8 cents, reflects the increased demand from the cold that has also propped up physical gas prices. The price run up comes in the face of government data that showed speculative investment funds last week had trimmed, at least temporarily, their net long position in natural gas futures, options and swaps for the first time in three months. Most traders, expecting milder weather to lead to more above-average weekly inventory builds, remain skeptical of further upside until hotter weather arrives and forces homeowners and businesses to crank up air conditioners. Commodity Weather Group said it expected U.S. temperatures to mostly range from normal to slightly above normal for the next two weeks, but no major heat was forecast for the period. ANOTHER BIG INVENTORY BUILD EXPECTED Data from the U.S. Energy Information Administration last week showed that total domestic gas inventories rose by 88 billion cubic feet to 1.865 trillion cubic feet. The weekly build was above the Reuters poll estimate of 83 bcf and well above the five-year average increase for that week of 69 bcf, and initially pressured prices. The gain was the fourth of the stock building season and exceeded market expectations for the second straight week. It trimmed the deficit versus the five-year average by 19 bcf, but stocks are still 99 bcf, or 5 percent, below that benchmark. That deficit is likely to shrink again in Thursday's EIA report. Injection estimates range from 90 to 106 bcf, with most in the mid-90s. Stocks rose 56 bcf during the same week last year. The five-year average increase for that week is 83 bcf. PRODUCTION CLIMBS DESPITE FEWER RIGS Baker Hughes data on Friday showed the gas-directed rig count fell last week by four to an 18-year low of 350. Despite the steep decline in dry gas drilling, production has not slowed much, if at all, from 2012's record highs. The EIA last week raised its estimate for domestic natural gas production in 2013, expecting output this year to be up about 1 percent from last year. If realized, it would be the third straight year of record production.