* Gas-directed rig count up for third straight week * Horizontal rigs slip for fifth time in six weeks * Oil rig count retreats for third time in four weeks NEW YORK, July 12 (Reuters) - The number of rigs drilling for natural gas in the United States rose this week for a third straight week, climbing by seven to 362, data from Houston-based Baker Hughes showed on Friday. Despite recent gains, the gas-directed rig count is still hovering just above the 18-year low of 349 posted three weeks ago. Producers have mostly been curbing dry-gas drilling in favor of more profitable crude oil and liquids-rich plays such as Eagle Ford in Texas and Marcellus in Appalachia. But the gas price run-up in early May to a 21-month high of $4.444 per million British thermal units stirred concerns that producer hedging at higher prices might keep dry gas flowing. Gas futures prices on Friday, which were up about 5 cents at $3.665 per mmBtu just before the data was released at about 1 p.m. EDT, slipped about 2 cents after the report. Front-month futures hit a 3-1/2-month low of $3.526 two weeks ago. The oil-focused rig count fell by four this week to 1,391. The oil rig count hit a nine-month high of 1,413 four weeks ago, Baker Hughes data showed. The oil count is down 36 rigs, or 2.5 percent, from the same week last year. Baker Hughes reported horizontal rigs, the type often used to extract oil or gas from shale, lost ground for the fifth time in six weeks, shedding 10 to 1,058. The horizontal count is down 11 percent from the record high of 1,193 set in May 2012. Drilling for natural gas has mostly been in decline for the last 21 months. The count is down about 61 percent since peaking in October 2011 at 936, but so far production has not slowed much, if at all, from the record high hit last year. The associated gas produced from shale oil and shale gas liquids wells has kept dry gas flowing at a brisk rate. The U.S. Energy Information Administration still expects gas output in 2013 to post a record high for a third year.