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Mr. Kerry praised Turkey for its generosity toward refugees and commitment to keeping its borders open, an issue of growing U.S. concern as the outflow of Syrians stretches the capacities of neighboring countries to accommodate them.

“The United States and Turkey will continue cooperating toward the shared goal of a peaceful transition in Syria,” he said.

Although given short shrift at the news conference, a U.S. official stressed ahead of Mr. Kerry‘s meetings that he also would urge the Turks to remain cautious over the contentious issue of Iraqi oil.

Turkey wants to import oil directly from Iraq’s autonomous Kurds in the north, a step that would enrage the central government in Baghdad and one the U.S. opposes. Washington doesn’t want the riches of Iraq to bring the country back to sectarian warfare and has urged that any export arrangement get the Iraqi government’s blessing.

The secretary of state is flying later Sunday to Israel, his third trip there in the span of two weeks. He’ll meet Palestinian President Mahmoud Abbas in Ramallah on the West Bank on Sunday night, followed by Mr. Netanyahu and other senior Israeli and Palestinian officials Monday as part of a fresh American bid to unlock the long-stalled Middle East peace process.

Conversations in Israel also will cover shared U.S. and Israeli concerns over Iran’s nuclear program. The U.S. and other world powers met the Islamic republic in Kazakhstan for another round of negotiations, but no breakthrough was announced on a proposed deal that would see international sanctions on Iran eased if Tehran convinces the world it is not trying to develop nuclear weapons.

Mr. Kerry said that the “door is still open” for a negotiated agreement but that the onus was on the Iranians.

“If you have a peaceful program for nuclear power, as a number of nations do, it’s not hard to prove that,” he said. “They have chosen not to live up to the international requirements and standards with respect to verification of their program.”

The other stops on his trip are Britain, South Korea, China and Japan. He returns to Washington on April 15.