* Gas-directed rig count climbs slightly after 14-year low * Horizontal rig count gains following 20-month low last week * Oil rig count rises to near 5-month high NEW YORK, April 12 (Reuters) - The number of rigs drilling for natural gas in the United States rose this week by two after posting a 14-year low the previous week, raising prospects that the recent rally in gas prices might be tempting some producers to bring on more supply. The gas-directed rig count edged up to 377 this week after sliding to 375 the previous week, its lowest since May 1999, 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 a 35 percent run-up in spot gas prices since mid-February, to a 20-month high of $4.249 per million British thermal units this week, has stirred expectations that gas output, still flowing near record highs, could increase in coming weeks. The oil-focused rig count jumped by 30 to near a five-month high of 1,387 this week, Baker Hughes data showed. The oil count is up 65 rigs, or 4.9 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, climbed by 18 this week to 1,102 after dipping to a 20-month low last week. The horizontal count is down 7.6 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 60 percent since peaking in 2011 at 936, but so far production has not shown any clear signs of slowing. The associated gas produced from more profitable shale oil and shale gas liquids wells has kept dry gas flowing at or near an all-time high. The U.S. Energy Information Administration expects marketed gas production to edge up slightly in 2013 to its third straight yearly record. Gas futures prices, which were up about 2 percent at $4.23 just before the Baker Hughes report, climbed to a 20-month intraday high of $4.249 after the rig data was released.