By Peter Apps

NICOSIA (Reuters) - Frustrated by a stalled process to reunite Cyprus, the de facto Turkish Cypriot state that has run the north for almost four decades says it is considering asking fellow Islamic states for formal recognition.

That would infuriate the Republic of Cyprus government, a European Union member that describes the north as being under illegal military occupation since a 1974 Turkish invasion. The eastern Mediterranean island has been divided ever since, with only Turkey so far recognizing the north as a sovereign state.

The discovery of considerable natural offshore natural gas deposits between Cyprus and Israel has further increased tension. The Turkish Cypriot side accuses the Cypriot government of acting unilaterally in inviting foreign firms to drill in the area. It says it wants to see some form of revenue-sharing from any gas production, an idea the Cypriot government rejects.

The Turkish Cypriot side say their first choice would be to negotiate reunification with the Greek Cypriot south, but that after decades of inaction it could not take forever.

If a deal proved impossible, the Turkish Cypriot side would have to respond, chief Turkish Cypriot presidential spokesman Osman Ertug told Reuters in an interview this week in the Turkish Cypriot part of the capital Nicosia.

That could mean going beyond the unilateral declaration of independence with which Turkish Cyprus announced it was seceding in 1983. "How do you go further? By getting recognition," he said.

Asked where such recognition might come from, Ertug - a veteran Turkish Cypriot negotiator who served as its representative to both Washington and the United Nations - would not name individual countries but said:

"From our Islamic brothers. We haven't aggressively sought recognition. But if things are not moving forward it is something we may have to do."

NEW OPENING

The election of a new Cypriot government last month offered a new opportunity for progress, according to Ertug.

"I would say the next few months are crucial. It is not just the gas. We have a new Greek Cypriot leader who says he is keen on talking. There seems to be willingness to talk when we call...," he said.

"Things can go either way. The gas can be a tool for cooperation or confrontation. But so far, I have to say it has made things worse."

The next step in the peace process, he said, should be for newly elected Cypriot President Nicos Anastasiades to meet Turkish Cypriot leader Dervis Eroglu informally at a social gathering in the next few months. That should lead, he said, to more talks aimed at reuniting the country while safeguarding the Turkish Cypriot minority and sharing gas deposits.

Turkish Cypriots say their economy has been throttled by years of trade sanctions that has left them struggling to keep pace financially with the rest of the island.

Last year, Turkey suggested it could absorb Turkish Cyprus entirely into the Turkish state if the peace process remains stalled. Such a proposal would alarm some Turkish Cypriots and Ertug said bluntly the annexation option was not on the table.

The Greek Cypriot government - which currently controls slightly less than two thirds of the island - says any attempt to gain greater recognition for Turkish Cypriot independence would severely damage attempts at reconciliation.

"Of course it worries us," said Andreas Mavroyiannis, permanent secretary at the Cypriot foreign ministry. "But this threat is there constantly. We had this again when we joined the European Union. It will not deter us from exercising our sovereign rights."

Racing to agree a financial bailout with the EU, European Central Bank and International Monetary Fund, the Cypriot government is keen to push forward gas exploration and production as quickly as possible.

Already working with U.S. firm Noble Energy on exploration, Cyprus this year granted France's Total, Italy's ENI and South Korea's KoGas drilling rights.

"They have some very good cards," Ertug said of the south. "They have the international recognition. They have the EU membership. Until the recent crisis, they had a much stronger economy. And now they have the gas."

(Editing by Mark Heinrich)