VIENNA, May 23 (Reuters) - Mexico supports an extension of OPEC's supply cuts as a way to stabilise oil markets and bring fresh investment into the country's growing energy sector, the Mexican deputy secretary for hydrocarbons said on Tuesday.

Aldo Flores-Quiroga said he believed members of the Organization of the Petroleum Exporting Countries should and would continue plans to coordinate oil production cuts into at least 2018. He did not say whether he preferred a six- or nine-month extension, which OPEC members are debating.

"Stable markets help provide a stable framework for investment, and that helps Mexico," said Flores-Quiroga, who assumed his post last summer.

Oil ministers from OPEC and non-member producers meet on Thursday in Vienna.

Mexico, which is not in OPEC, has seen its oil industry atrophy in the past 50 years due to underinvestment and hostile regulation of foreign partners.

Constitutional changes in 2013 have slowly begun to attract capital to the second-largest Latin American economy, but low oil prices CLc1 LC0c1 have hindered Mexico City's efforts.

Exxon Mobil Corp XOM.N , for example, plans to invest $300 million in retail filling stations through the next decade in Mexico, but will import fuel due to a lack of local crude supply and refining capacity.

(Reporting by Ernest Scheyder; Editing by Dale Hudson) ((ernest.scheyder@thomsonreuters.com; Twitter: @ErnestScheyder; +1-713-210-8512; Reuters Messaging: ernest.scheyder.thomsonreuters.com@reuters.net))