LONDON, May 24 (Reuters) - OPEC is focusing on market share rather than on supporting oil prices, Iraq's OPEC governor said on Tuesday in comments that will dampen expectations that OPEC might agree steps to support prices at a meeting next week.

"After two years, the market is starting to balance but it nearly destroyed many countries," Falah Alamri, Iraq's OPEC governor and head of the State Oil Marketing Organisation (SOMO), said at an Iraq oil conference in London.

The "two years" is a reference to OPEC's meeting in November 2014, when the producers group refused to cut output to support prices.

"Now OPEC focuses on market share, which means they do not want to interfere with the price," Alamri said.

OPEC meets to set policy on June 2.

(Reporting by Alex Lawler and Ahmad Ghaddar; editing by Jason Neely) ((alex.lawler@thomsonreuters.com; +44 207 542 4087; Reuters Messaging: alex.lawler.reuters.com@reuters.net))