* Front futures rebound after 3 straight weekly declines * Moderating weather seen slowing demand for next 2 weeks By Joe Silha NEW YORK, May 13 (Reuters) - Front-month U.S. natural gas futures, backed by a chilly start to the week in the Northeast that lifted demand, ended higher on Monday, but gains appeared capped by the milder outlook for later this week and next that should slow demand. Gas prices had lost ground in three previous weeks, sliding more than 11 percent as moderating spring weather curbed heating needs. The milder turn in temperatures followed a cold winter and chilly spring that whittled down record high inventories and drove gas prices up more than 40 percent from mid-February lows during nine straight weeks of gains. Chart traders agreed the market was oversold and due for a bounce, noting prices recently have tested technical support in the $3.90 per mmBtu area but so far have not been able to settle below that level. But with expectations that milder weather will lead to above-average weekly inventory builds, few traders expect much upside until hotter weather arrives and forces homeowners and businesses to crank up air conditioners. "We're not seeing heat building in Texas and the Southeast yet, which should mean larger storage injections, but it doesn't look like they want to push prices much lower right now," said Teri Viswanath, analyst at BNP Paribas in New York. Front-month gas futures on the New York Mercantile Exchange ended up 1.5 cents at $3.925 per million British thermal units after trading between $3.886 and $3.977. 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 also noted signs that speculative investment funds may be giving up on the recent bull run, at least temporarily. Last week they trimmed their net long position in natural gas futures, options and swaps for the first time in three months, according to government data released on Friday. Commodity Weather Group said it expected the weather pattern for the next two weeks to remain too quiet to generate any large-scale demand concerns, except in Southern California, where temperatures could again top 100 degrees Fahrenheit. ANOTHER BIG INVENTORY BUILD 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, which was the fourth of the stock building season and exceeded market expectations for the second straight week, trimmed the deficit versus the five-year average by 19 bcf, leaving stocks at 99 bcf, or 5 percent, below that benchmark. Early injection estimates for Thursday's EIA report range from 88 bcf to 106 bcf versus a 56-bcf build during the same week last year and a five-year average rise for that week of 83 bcf. PRODUCTION CLIMBS DESPITE FEWER RIGS Baker Hughes data on Friday showed the gas-directed rig count fell last week by four to 350, its lowest since June 1995. Despite the steep decline in dry gas drilling, production has not slowed much, if at all, from 2012's record highs. The EIA on Tuesday 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.