* Gas-directed rig count hits lowest since June 1995 * Horizontal rigs climbs for second straight week * Oil rig count up for sixth time in seven weeks NEW YORK, May 10 (Reuters) - The number of rigs drilling for natural gas in the United States fell this week for the third straight week, hitting its lowest level in nearly 18 years as producers continued to pull back from dry gas drilling. The gas-directed rig count slid by four this week to 350, its lowest since June 1995, when the count stood at 340, data from Houston-based Baker Hughes showed on Friday. Producers have mostly been curbing dry-gas drilling in favor of more profitable oil and liquids-rich plays such as Eagle Ford in Texas and Marcellus in Appalachia. But the 40 percent run-up in spot gas prices since mid-February to a 21-month high of $4.444 per million British thermal units just last week, had stirred concerns that gas output, still flowing at or near record highs, could increase in coming weeks. Prices have since slipped to the $3.90s. The oil-focused rig count rose for the sixth time in seven weeks, climbing by nine to an eight-month high of 1,412, Baker Hughes data showed. The oil count is up 40 rigs, or 2.9 percent, from the same week last year. Baker Hughes also reported that horizontal rigs, the type often used to extract oil or gas from shale, gained seven this week to 1,099. The horizontal count is still down 7.9 percent from the record high of 1,193 set last May. Drilling for natural gas has mostly been in decline for the last 18 months. The count is down about 63 percent since peaking in 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 more profitable shale oil and shale gas liquids wells has kept dry gas flowing at a brisk rate. On Tuesday, the U.S. Energy Information Administration raised its estimate for domestic natural gas production in 2013, expecting output this year to be up about 1 percent from last year. If realized, it would be the third straight year of record production. Gas futures prices, which were down about 5.8 cents in the $3.925 area just before the Baker Hughes data was released, were little changed from that level after the report.