* Graphic: Global asset performance tmsnrt.rs/2yaDPgn * Graphic: World FX rates tmsnrt.rs/2egbfVh LONDON, Aug 30 (Reuters) - World stocks hovered around record highs on Monday, confident the U.S. Federal Reserve is no rush to step away from massive stimulus, while oil prices fell as Hurricane Ida weakened after forcing precautionary shutdowns of U.S. Gulf oil production. Major European bourses were broadly steady, as were U.S. stock futures, and overall trade was subdued with London out for a public holiday. The Europe-wide STOXX 600 traded flat, but was on course to end August with a more than 2% rise - its seventh straight month of gains in what would be its longest such winning run in over eight years. Asian stocks rallied to a two-week high and Japan’s blue-chip Nikkei closed up 0.5%, leaving MSCI’s world stock index hovering at record highs. Underpinning positive sentiment in global equity markets was Friday’s Jackson Hole speech by Federal Reserve Chair Jerome Powell in which he said tapering of stimulus measures could begin this year, but added the central bank would remain cautious. “Powell broke little new ground on the Fed’s outlook for the economy and its likely policy path,” said Mark Haefele, chief investment officer at UBS Global Wealth Management. “However, it did have a dovish tilt, with clear investment implications that support the continuation of the reflation trade.” OIL FALLS Oil prices headed lower, meanwhile, pulling back from a four-week high as Hurricane Ida weakened into a Category 1 hurricane within 12 hours of coming ashore and attention turned to an OPEC meeting on Wednesday to discuss a further output boost. Nearly all U.S. offshore Gulf oil production, or 1.74 million barrels per day, was suspended in advance of the storm. Brent crude futures were down 47 cents, or 0.7%, at $72.19 a barrel. They rose more than 11% last week in anticipation of disruptions to oil production from Hurricane Ida. U.S. oil fell 1.2% to $67.95 a barrel, having jumped a little more than 10% over the last week. “Hurricane Ida will dictate oil’s near-term direction,” said Jeffrey Halley, senior market analyst at OANDA. “If Ida weakens and its path of destruction is lower than expected, oil’s rally will temporarily lose momentum here.” OPEC+ is likely to keep its oil output policy unchanged when the group meets on Wednesday and continue with its planned modest production increase, three OPEC+ sources told Reuters. In fixed income and currency markets, it was the Fed’s dovish tone that continued to hold sway, with focus turning to Friday’s key U.S. non-farm payrolls report. The yield on benchmark 10-year Treasury notes was around 1.2 basis points lower at 1.30%. And the dollar index, which measures the greenback against a basket of currencies, was fairly steady at a two-week low, having fallen 0.4% after Powell’s remarks. The euro was steady at $1.1800, having touched a three-week peak earlier in the session, while the dollar was little changed at 109.83 yen. “If we get a (U.S. payrolls) number close to a million that would increase the odds of taper being announced in September, but if the number is line with expectations then there’s a 50-50 chance for a September move,” said Vasileios Gkionakis, global head of FX strategy at Lombard Odier Group. Elsewhere, gold was just a touch lower at $1,814.6 per ounce, having touched its highest in three weeks earlier in the session. Reporting by Dhara Ranasinghe Additional reporting by Alex Lawler Editing by Mark Potter Our Standards: The Thomson Reuters Trust Principles.