* Gas-directed rig count slides to new 14-year low * Horizontal rig count falls to lowest in nearly 20 months NEW YORK, April 5 (Reuters) - The number of rigs drilling for natural gas in the United States fell this week to the lowest since May 1999, as producers continued to pull back from dry gas drilling despite strong price gains over the last six weeks. The gas-directed rig count, which slid by 14 this week to 375, eclipsed the previous 14-year low of 389 posted last week, according to data from Houston-based oil services firm Baker Hughes Inc 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 30 percent run-up in spot gas prices since mid-February to a 19-month high of $4.124 per million British thermal units this week has stirred expectations that gas output, still flowing at or near record highs, could increase in coming weeks. The oil-focused rig count rose by three to near a four-month high of 1,357 this week, Baker Hughes data showed. The oil count is up 28 rigs, or 2.1 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, dropped by 15 this week to a new 20-month low of 1,084. The horizontal count is down 9.1 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 in 2013 to hit a record high for the third straight year. Gas futures prices, which were up about 4 percent at $4.105 just before the Baker Hughes report, climbed to a 19-month intraday high of $4.124 after the data was released.