By Nick Trevethan SINGAPORE (Reuters) - NYMEX crude rallied more than $1 to $72.40 a barrel on Thursday, up for a fourth day running, lifted by a soft dollar, gains in equities markets and soothing words from OPEC. Asian stock markets pushed higher and the euro edged up versus the dollar. On the fundamental side, a fall in U.S. crude stocks five times greater than analyst forecasts on Wednesday and positive comments on prices and the economy by Saudi Oil Minister Ali al-Naimi also supported the price. OPEC left output unchanged, as expected, with Naimi saying prices were being driven by economic recovery, and that high levels of inventory had become irrelevant to the market. "The lack of more aggressive action reflected a belief that demand will be sufficient in pulling down the overhang in the market," David Kirsch, director of market intelligence services at PFC Energy in Washington, said. "It's a shift from previous OPEC policy in being more proactive against their downside risks and obviously the state of the economy played a part in this decision." NYMEX crude for October delivery stood at $72.34 a barrel by 2:30 a.m. EDT, up $1.03 from Wednesday's settlement. London Brent crude rose 80 cents to $70.63 a barrel. Traders noted rising interest in front-month WTI versus longer dated futures in the past month or so and a narrowing in the contango, or discount for near-dated oil. "The one lesson we all learnt from the great price crash is that all markets are correlated. The gains we are seeing in oil right now are driven by equities as much as anything and people are buying prompt crude to ride the wave we are seeing in stocks," a Sydney-based energy trader said. For a graphic showing WTI crude versus equities, click: here Asian share markets were underpinned by a 0.5 percent gain in the Dow Jones industrial average .DJI and the Federal Reserve's Beige Book survey, which showed the U.S. economy was stabilizing, although many key sectors remained weak. That buoyed sentiment in Japan, where the Nikkei index .N225 gained 1.4 percent even though machinery orders' data pointed to weak capital spending in the world's No. 2 economy. Also bullish was a big fall in U.S. crude stocks, with the American Petroleum Institute reporting a 7.2 million barrels drawdown in the week to September 4, far more than the 1.5 million barrels forecast in a Reuters poll. However, this was partly offset by a 3.3-million-barrel jump in distillate stocks, far exceeding the forecast for an increase of 800,000 barrels, while gasoline stocks rose 571,000 barrels against the forecast for a 1.3 million barrel drawdown. More inventory data is expected on Thursday with the Energy Information Administration's report at 11 a.m. EDT.

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