One option under study is to build a $10 billion liquefied gas terminal in nearby Cyprus, which also has found gas, and jointly export to Europe.
But that's risky because of Turkey's occupation of the northern part of the largely Greek-speaking island and Ankara's insistence the Greek sector cannot drill without a political settlement.
Turkey used to be Israel's bosom ally, but their two-decade strategic alliance fell apart in May 2010 after Israel's navy jumped Turkish ships carrying humanitarian aid to the Israeli-blockaded Gaza Strip, killing nine Turks.
A second option is to make nice with Ankara and build an undersea pipeline to Turkish terminals, to export to gas-hungry Europe.
Now there seems to be a third option: encourage Turkey and Cyprus to settle their dispute, triggered by Turkey's invasion of northern Cyprus in 1974 and its establishment of a maverick Turkish Republic of Northern Cyprus only Ankara recognizes.
Since Israel, which began producing gas from its Tamar field March 30, is way ahead of Cyprus, Lebanon and Turkey in terms of developing the east Mediterranean's massive energy reserves, it has considerable influence concerning what comes next.
"Israel is quietly challenging Turkey and Cyprus to make a choice: move together to develop Israel's share of the East Mediterranean's natural gas riches, or stay on the sidelines and perpetuate their decades-old stalemate over Cyprus," observed analyst Hugh Pope, Turkey-Cyprus director of the International Crisis Group, a conflict resolution group in Brussels.
"Israel has stated its preference for export pipelines to both Turkey and Cyprus, and is in a strong position to elicit both countries' cooperation: only Israel has big proven reserves, while test drillings are still trying to establish whether Cyprus has major exportable quantities."
In June, the Israeli government ruled that 40 percent of the Jewish state's gas production, once that's fully under way, will be allocated for export.
It also said it could supply a liquefied natural gas plant, to convert the gas to liquid for transportation by tanker, outside Israel, with Cyprus the only likely location.
This moved the export issue forward, without specifying a final decision. But this month, Israel's energy envoy, Michael Lotem, fleshed out the government's thinking on an issue that will impact greatly on Israel's economic development as a key regional energy producer.
"An energy facility [in Cyprus] has less complications than other options," he told an international gathering of energy executives in the Cypriot resort of Paphos.
This would make the Greek Cypriots happy since, with their economy on the floor because of the eurozone crisis, they seek salvation by becoming a regional energy hub.
However, Lotem stressed that Israel favors having "more than one energy destination."
Turkey has no energy resources of its own, but sees itself as a key regional energy hub between east and west, while acquiring energy supplies for itself.
Israeli and Cypriot gas could feed into the Trans Anatolia Natural Gas Pipeline that Azerbaijan and others plan to build across Turkey, or the Trans Adriatic Pipeline that European and Azerbaijani companies seek to build from Turkey's border with Greece, across the Balkans and then to Europe.
The numbers are there. Israel's current gas reserves total 25-30 trillion cubic feet. Cyprus, still in the early exploration phase, claims it has 60 tcf.
The U.S. Geological Survey said in 2010 the Levant Basin, which covers Israel, Cyprus, Syria, Lebanon and the Gaza Strip, contains an estimated 123 tcf.
Cyprus' Turkish and Greek business communities, and probably quite a few government officials as well, would likely welcome an end to the bitter confrontation. But there are deep-rooted hatreds and suspicions on both sides.
The Greek Cypriots reportedly rule out allowing a pipeline to Turkey through their exclusive economic zone until there's been a settlement.
Israel's not likely to agree to a costly LNG plant on Cyprus if there's no pipeline to Turkey. It wants a firm answer by early 2014.
Meantime, Istanbul-based Pope observes, "there's no sign yet that Turkey's mercurial, anti-Israel prime minister, Recep Tayyip Erdogan, would approve a pipeline that might help Israel."
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