Turkey does not recognise the Nicosia government, seen by the rest of the world as Cyprus' sole authority, and wants offshore exploration to await a peace settlement between the Greek and Turkish communities, estranged since a 1974 Turkish invasion of the north of the island.
Although Turkey has few oil and gas reserves of its own, the NATO member retains leverage because of its substantial navy and its role as an important transit hub for energy from Russia and the Caspian Sea region.
"Companies that cooperate with (Greek Cypriots) will not be included in future energy projects in Turkey," the Foreign Ministry said in an e-mailed statement.
"Turkish Cypriots have the same, indissoluble rights as Greek Cypriots to the natural resources of the island's continental shelf," it said. "Both communities must decide together how maritime natural gas and oil resources will be used."
French oil major Total, Malaysia's Petronas, Korea's Kogas, Eni of Italy, Russia's Novatek , Delek of Israel and Australia's Woodside Energy Holdings are among the 15 companies who have bid for contracts.
Cyprus, along with Israel and Lebanon, straddle what may be the biggest natural gas find of the past decade in the politically volatile eastern Mediterranean.
Nicosia says any exploration is within its rights, and has received backing from its partners in the European Union.
Turkey, which has also begun exploration work off its Mediterranean coast, sits on strategic energy routes to lucrative Western markets. Eni is part of a venture that wants to build a 340-mile pipeline, worth $3 billion, to ship Russian gas to world markets.
The potential of the eastern Mediterranean deposits is enormous. U.S.-based Noble Energy last year reported 5-8 trillion cubic feet (tcf) of gas south of Cyprus -- enough to make Cyprus self-sufficient for 250 years.
Turkey responded to Noble's exploration by sending out a seismic research vessel accompanied by military escort.
The question of who has the right to tap the deposits, which could total more than 100 tcf, has added urgency to efforts to settle the conflict over Cyprus and has also brought Lebanon into dispute with Israel over the Jewish state's discoveries.
Most of the interest shown by bidders this month was for a block lying northeast of the recently discovery on the maritime border between Cyprus and Israel.
The Turkish Foreign Ministry said the Cypriot tender included a western area that abuts Turkey's continental shelf.
"As Turkey has previously stated, it will not allow any activity in that area," the statement said.
Only Turkey recognises the Turkish Cypriot administration and keeps tens of thousands of troops on the island, located some 40 miles off its southern coast.
The decades-long dispute has threatened to derail Turkey's bid to join the European Union. A member since 2004, Cyprus takes over the bloc's rotating presidency in July, and Turkey has said it will suspend its candidacy during that tenure.
Efforts to reconcile Greek and Turkish Cypriots have failed more than a dozen times since the 1960s. The two sides are now currently engaged in another round of UN-backed negotiations.