JERUSALEM (Reuters) - Israel set terms for concluding a peace deal with Syria on Thursday, closing ranks with Washington in demanding Damascus distance itself from Iran and stop supporting Palestinian and Lebanese militants.

Coordinated announcements on Wednesday by Israel and Syria that they had begun indirect talks in Turkey, the first confirmation of negotiations between the long-time enemies in eight years, drew a lukewarm response from the United States.

Many analysts say U.S. hostility to Damascus, and to its Iranian and Lebanese Hezbollah allies, makes a Syria-Israel deal unlikely before President George W. Bush steps down in January.

Summing up three days of discussions in Istanbul, Turkish Foreign Minister Ala Babacan said both sides were satisfied they had found “shared ground”. He said future talks would be held periodically in Turkey.

“The Syrians know what we want and we know what they want,” Israeli Prime Minister Ehud Olmert said in Jerusalem. Olmert revealed the talks two days before he faces a second round of police interrogation over graft allegation.

Syria is demanding the return of the Golan Heights, a plateau overlooking Damascus on one side and the Sea of Galilee on another, since Israel captured the strategic territory in the 1967 Middle East war.

Syrian Information Minister Muhsin Bilal condemned Israel’s setting of any prior conditions.

“These conditions have already been rejected as is the phrase ‘difficult concessions’ as what the Syrians are demanding is their right,” Bilal told Al Jazeera television.

Olmert, who recently took a vacation on the Golan Heights, has not said publicly that Israel would give up all of the area. But he has spoken of “difficult concessions” Israel would have to make in any land-for-peace accord with Syria.

Echoing U.S. comments, Israeli Foreign Minister Tzipi Livni said Syria needed to “distance itself completely” from “problematic ties” with Iran.

Syria, she told reporters, must also stop “supporting terror -- Hezbollah, Hamas”, groups backed by the Islamic Republic.

Israeli Defense Minister Ehud Barak, who as prime minister in 2000 took part in U.S.-hosted talks with Syria that failed over the key issue of the future of the Golan Heights, said in a speech that both sides would have to make “painful concessions”.

No U.S. OBJECTION

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The United States, in its initial public reaction to Israeli-Syrian contacts, said it did “not object” to talks but repeated its criticism of Syria’s “support of terrorism”.

The United States and Israel consider Hamas a terrorist organization. The Islamist group, which seized control of the Gaza Strip last June, opposes statehood talks between Olmert and Palestinian President Mahmoud Abbas that Washington hopes can result in a deal by year’s end.

Palestinian Prime Minister Salam Fayyad, speaking in the occupied West Bank, said he was not worried Israel would pursue peace with Syria at the expense of progress in the U.S.-brokered negotiations with the Palestinians.

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“The concern is if the (Israeli-Palestinian) political process ... does not proceed at the pace necessary,” Fayyad told reporters. “I hope other tracks are moving and moving well.”

Olmert, who revealed the discussions with Syria two days before he faces a police interrogation over bribery allegations he has denied, said peace efforts would be lengthy and complex.

A television poll found 70 percent of Israelis oppose giving back the Golan Heights to Syria, and a majority also believed Olmert was using the talks to distract from the criminal investigation that could force him from office.

“Everyone knows that Olmert wants to end his term on a diplomatic note, not a criminal one. The question is, what will come first -- an indictment or a peace treaty,” columnist Yossi Verter wrote in newspaper Haaretz.

Barak, leader of Israel’s centre-left Labor Party, said peace with Syria could be achieved only from a position of strength and self-confidence.

Eight months ago, Israeli jets bombed what U.S. officials described as a North Korean-built nuclear facility in Syria.

Syrian Foreign Minister Walid al-Moualem said Israel had shown that it might return the plateau. “Without this commitment we cannot conduct any negotiation,” he told Reuters.

The Israeli-Syrian talks in Shepherdstown, West Virginia in 2000 broke down over control of the shore of the Sea of Galilee, where Israel draws much of its water.

Among Olmert’s vast army of domestic critics, supporters of the 18,000 Jewish settlers in the Golan Heights threatened to bolt his fragile coalition if he tries to give up the territory.

Others wondered aloud if Wednesday’s announcement was not timed to divert attention from Olmert’s troubles with the police. They will interview him for a second time, on Friday, over suspicions he took bribes from an American businessman.

Olmert has said he would resign if indicted.