LAGOS, June 7 (Reuters) - OPEC and its allies expect oil inventories to fall further in the coming months, OPEC's secretary general said on Monday, suggesting efforts by the producers to support the market are succeeding.

Oil stocks in the developed world nations fell by 6.9 million barrels in April, Mohammad Barkindo said in a virtual appearance at the Nigeria International Petroleum Summit, 160 million barrels lower than the same time one year ago, making the figure public for the first time.

"We expect to see further drawdowns in the months ahead," he said. (Reporting By Alex Lawler and Libby George; editing by David Evans)