VIENNA/LJUBLJANA, Feb 2 (Reuters) - Austrian stock market operator CEESEG said on Tuesday it will raise its stake in the Ljubljana stock exchange to more than 97 percent, from 81 percent, after Slovenia's top court had ordered it to launch a full buyout offer.

The country's Supreme Court on Monday backed an earlier order by Slovenian market regulator ATVP, which had told CEESEG to buy the rest of the Ljubljana stock exchange at the same price at which it bought its initial stake.

CEESEG, formerly known as Wiener Boerse, said it may appeal against the court ruling but reiterated it was still interested in buying out minority shareholders of the Ljubljana bourse but did not at what price it had agreed to buy its additional stake.

CEESEG owns the stock exchanges in Vienna, Ljubljana, Prague and Budapest. It bought 81 percent of the Ljubljana bourse in June 2008. ATVP removed CEESEG's voting rights later that year, demanding that it launch a full takeover bid for the bourse.

Under the order CEESEG would have had to bid 1,401 euros ($1,949) per share for the remaining stake, the same price it paid for its 81 percent stake, or reduce it below 25 percent.

CEESEG had appealed against the ATVP order, claiming the deal predated Slovenia's new takeover legislation. The court however threw out the complaint and sided with the regulator. ($1=.7188 euros) (Reporting by Marja Novak in Ljubljana and Boris Groendahl in Vienna; Editing by Greg Mahlich)