NEW YORK, June 24 (Reuters) - U.S. natural gas futures, backed by hotter weather in the Northeast and Midwest early this week, edged higher on Monday, but the milder trend in the extended outlook helped limit the upside. "Gas prices have rebounded back to the upside amidst light short-covering as this month's bidweek trading begins. Weather forecasts, after the next couple days of above-normal temperatures across the Midwest and Northeast, are cooler for the first half of July," Addison Armstrong, senior director of market research at Tradition Energy, said in a report. Prices sold off a bit late last week, but the front month managed to eke out a 1 percent gain for the week, its first weekly gain after sinking 12 percent in the previous three weeks. But without a sustained, broad-based heatwave, many traders remained skeptical of any move up with inventories comfortable and gas production still flowing at or near a record high. While heat is forecast for Texas and the West later this week and next week, MDA Weather Services expects seasonal or below seasonal temperatures to dominate the eastern half of the nation during the six-to-10-day time frame. At 9 a.m. EDT (1300 GMT), July front-month gas futures on the New York Mercantile Exchange, which expire on Wednesday, were up 2.9 cents at $3.80 per million British thermal units after trading between $3.725 and $3.822. The front contract posted a three-month low of $3.71 nearly two weeks ago. Baker Hughes data on Friday showed the gas-directed rig count fell last week by four to an 18-year low of 349. Despite a steep decline in dry gas drilling over the last 20 months, production has not slowed much, if at all.