* Milder Northeast, Midwest weather expected to slow demand * Tropical Storm Dorian remains over central Atlantic-US NHC By Joe Silha NEW YORK, July 26 (Reuters) - U.S. natural gas futures ended lower for the third straight session on Friday, undermined by fairly mild weather forecasts for the next two weeks that should slow air conditioning demand. The front-month futures contract finished this week down 6.2 percent, its first weekly loss in four weeks and its biggest weekly decline in eight months. The contract posted a four-week high of $3.835 per million British thermal units late last week. Traders were watching Tropical Storm Dorian, located in the central Atlantic Ocean, but many did not expect the storm to significantly disrupt Gulf of Mexico energy operations. Some forecasters see the system weakening as it tracks west-northwest toward the Bahamas and then toward southern Florida by late next week. Many traders remain skeptical about higher futures prices, with inventories comfortable, production still flowing at or near a record high and no extreme heat on the horizon to kick up demand. "The weather has been the story this week. We've got bearish weather and it looks like that's going to continue for the next couple of weeks. Unless the forecasts change, we could break below the $3.526 (per mmBtu) low from late June," Steve Mosley at The SMC Report in Arkansas said. Front-month August gas futures on the New York Mercantile Exchange, which expire on Monday, ended down 8.9 cents, or 2.4 percent, at $3.555 per million British thermal units, after trading between $3.548 and $3.654. Futures open interest, or the number of longs or shorts outstanding, fell more than 43,000 contracts, or 3 percent, in the first four sessions this week, indicating that long liquidation, not new selling, helped back the move lower. While inventory builds reported by the Energy Information Administration have fallen below average for two straight weeks, many traders expect mild temperatures ahead to open the door to much bigger injections in coming weeks. Early build estimates for next week's storage report range from 51 billion cubic feet (bcf) to 61 billion cubic feet. Stocks rose by 28 bcf during the same year-ago week, while the five-year average increase for that week is 47 bcf. Total domestic gas inventories of 2.786 trillion cubic feet are hovering just 1.6 percent below the five-year average, according to EIA data released on Thursday. Forecaster MDA Weather Services still expects temperatures for the eastern half of the nation to mostly range from normal to below normal for the next two weeks. Baker Hughes data on Friday showed the gas-directed rig count was unchanged this week at 369 following four straight weekly gains. While the count remains not far above the 18-year low of 349 posted late last month, the EIA still expects gas output in 2013 to hit a record high for a third straight year.