A US-brokered thaw between Turkey and Israel could alter the energy equation in the eastern Mediterranean, in theory allowing newly discovered Israeli gas to be piped to import-dependent Turkey and on to other markets.
Israel, once energy poor, is expected to become a gas exporter by the end of the decade. Its huge offshore Leviathan field contains an estimated 17 trillion cubic feet (tcf) of gas, making it the world's largest offshore discovery of the past decade when it was found in 2010.
Seventeen trillion cubic feet (481 billion cubic meters) is equivalent to almost a year's worth of European gas demand and enough to cover Israel's gas needs for generations.
US President Barack Obama last month brokered a first step in reconciliation between the two former allies, whose relations were frozen after the 2010 killing by Israeli marines of nine Turks aboard a Gaza-bound aid ship.
Prime Minister Benjamin Netanyahu apologized to his Turkish counterpart Tayyip Erdogan over the killings and pledged compensation to the bereaved, meeting a long-standing Turkish demand. Turkey, for its part, appeared to back off a separate demand that Israel stop blockading Gaza.
"The reason for Israel's apology was not energy projects. But the consequence could be energy projects," Yildiz told reporters at an energy conference in Ankara.
"We have said we are not closed to these in the future. But at this stage ... it is early to talk about energy projects."
Because Israel's domestic energy market is so small, exports are key to the development of the find. It would be cheaper to export gas via a pipeline to Turkey than converting it to liquefied natural gas to reach export markets by ship.
Turkey could become a large consumer of Israeli gas and serve as a transit route to other export markets, but there are concerns, behind the conciliatory rhetoric, about how quickly Turkish-Israeli relations will be restored.
US Secretary of State John Kerry urged the two nations to restore full relations during a trip to Istanbul on Sunday, saying such a move was vital to regional stability.
Despite Obama having pulled off a diplomatic coup – a three-way telephone call with the Israeli and Turkish prime ministers, who had not spoken since 2011 - some officials in Washington are worried Turkey might be backtracking on the deal.
An Israeli delegation had been due in Turkey this week to begin discussing details of the compensation agreement, but Turkey postponed the meeting due to a foreign trip by a senior government official who is involved in talks with Israel.
Neither country has said when their ambassadors would go back, a prerequisite for the restoration of relations necessary for bilateral energy talks.
Yildiz also said that Turkey wanted to see the Iraqi constitution respected in any deals between energy firms and the northern Iraqi Kurdistan region.
He told Reuters in an interview last week that he saw no obstacles to public or private firms striking oil exploration deals with Kurdistan and that Turkey would play an active role in any arrangement under which crude export revenues are shared between the central government and Kurdistan.
Yildiz added that Turkey's state oil company TPAO had applied for exploration rights off the coast of Lebanon, which shares a border with Israel. Israel and Lebanon have never agreed upon a maritime border.
"For the field offshore Lebanon, several firms have applied including TPAO. We're hoping to hear on the pre-qualification results soon and we hope TPAO will be one of them," Yildiz said.
"TPAO will participate in the Lebanon (project)." Dozens of companies have submitted pre-qualification bids to explore for oil and gas in Lebanon's offshore waters.
Interest in drilling in the eastern Mediterranean has grown since natural gas fields were discovered off Israel.
Names of the pre-qualified companies will be announced on April 18 and the government aims to agree its first exploration and production agreement by February next year.