* Cool near-term forecasts pressure front-month prices * Warmer extended weather outlook limits downside * Coming up: EIA, Enerdata natural gas storage data Thursday By Joe Silha NEW YORK, May 22 (Reuters) - Front-month U.S. natural gas futures closed lower on Wednesday for the first time in four sessions, as prices pulled back ahead of Thursday's inventory report and in the face of cooler weather heading into a holiday weekend that should slow demand. Offices for most trading firms will be closed on Monday for the U.S. Memorial Day holiday. Traders said the market was due for a pullback after rising nearly 7 percent in the previous three sessions. "The market has been range trading. Next week looks like there may be some moderate cooling demand, but it might not be enough to kick prices up significantly," said Jonathan Lee at Ecova Inc in Spokane, Washington. Front-month gas futures on the New York Mercantile Exchange ended down 0.6 cent at $4.186 per million British thermal units after trading between $4.155 and $4.228. The front contract is still up 3.2 percent so far this week. Ecova's Lee said profit taking ahead of the U.S. Energy Information Administration's weekly storage report on Thursday might also have pressured front-month prices. Traders and analysts polled by Reuters are expecting to see that total gas stocks rose 91 billion cubic feet last week. That would be well above the 75 bcf injection during the same week last year, but nearly flat with the 90-bcf five-year average increase for that week. Inventory builds have exceeded market expectations for three straight weeks as mild May weather slowed overall demand. Chart traders agreed the market seemed well supported in the low-$3.90s after testing and holding that area several times last week. But with supplies still comfortable, many traders remain skeptical of the upside, at least until a broader-based heat wave forces more air conditioning loads. Seasonal or below seasonal temperatures are expected for the eastern half of the nation for the next five days, but Commodity Weather Group noted the first week of June turned hotter for the Midwest and East, with heat also spilling into the South. Traders noted that deep deferred futures finished with modest gains, with 2018 contracts ending about 3 cents higher. Back months have mostly outperformed over the last few days following news on Friday that the U.S. Energy Department approved natural gas exports from Freeport LNG's Texas terminal. Despite a steep decline in dry gas drilling over the last year and a half, production has not slowed much, if at all. The Energy Information Administration still expects output in 2013 to post a record high for a third straight year.