NEW YORK, June 25 (Reuters) - U.S. natural gas futures slipped slightly early Tuesday, as milder forecasts for later this week and next week that should slow demand outweighed heat in the Northeast and Midwest early in the week. Front-month gas futures have lost nearly 6 percent in the previous three trading sessions amid signs that the extended weather outlook was trending milder. It was the biggest three-day slide for the near month in seven weeks. At 9:15 a.m. EDT (1315 GMT), front-month July gas futures on the New York Mercantile Exchange, which expire on Wednesday, were down 1.5 cents at $3.724 per million British thermal units after trading between $3.718 and $3.76. The front contract posted a three-month low of $3.71 two weeks ago. "Prices have dropped below $3.75 for a second time this month as the market searches for a bottom, but growing cooling demand and hurricane season risk should provide support in the coming weeks," Addison Armstrong, senior director of market research at Tradition Energy, said in a report. The front month eked out a small gain last week, its first after sinking 12 percent in the previous three weeks, but many traders remained skeptical of the upside without a sustained, broad-based heatwave, particularly with inventories comfortable and gas production still flowing at or near a record high. While heat is forecast to continue in the West for the next two weeks, MDA Weather Services expects near seasonal or below seasonal temperatures to dominate the eastern half of the nation during the six-to-15-day time frame. The Baker Hughes gas drilling rig count fell to another 18-year low last week, but U.S. gas production has not slowed much, if at all this year. The Energy Information Administration still expects gas output in 2013 to post a record high for a third year.