US President Barack Obama strolled among the ancient Jordanian ruins at Petra on Saturday, on the final leg of a four-day Middle East tour dominated by his embrace of Israel.

Obama flew by helicopter to view the rose-coloured stone ruins of the ancient Nabataean city, after winds from a sandstorm abated and allowed him to make the 55-minute trip across the plains and mountains of Jordan.

On Friday, high winds in Israel forced Obama to take his motorcade instead of his Marine One chopper to visit the Church of the Nativity in Bethlehem, and there had been fears his jaunt to Petra would be scrapped.

The US president, on the first foreign journey of his second term, emerged into a sunlit square facing the iconic Treasury building at Petra, carved out of the towering walls of sandstone rocks in southern Jordan.

"This is pretty spectacular," Obama, in a blue windbreaker, sweater, khaki pants and sunglasses said, peering up at the rocky cliffs.

"It's amazing. Spectacular."

Obama arrived at the ruins through a famous tunnel squeezed through rock formations, and was led through the World Heritage Site by Dr Suleiman al-Farajat, a University of Jordan tourism professor.

The visit to Petra, Jordan's most visited tourist site, wrapped up a four-day stay in the Middle East designed to assure Israel he is serious about its defence from Iran and to keep Israeli-Palestinian peace hopes alive.

Obama also warned on Friday that he was worried that Syria could become an enclave of "extremism" as his own policy towards the vicious sectarian war threatening to tear the nation apart came under scrutiny.

"(Extremists) are very good about exploiting situations that, you know, are no longer functioning. They fill that gap," Obama said at a news conference with King Abdullah II.

Obama's reluctance to arm opposition groups in Syria, fearing they are, or could transform into, extremist Islamist foes with links to Al-Qaeda, dogged him during questioning by journalists.

On Friday, a Jordanian reporter asked him why superpower America had no plan to end the killing in Syria, prompting Obama to defend US diplomatic efforts to isolate Syria and to note hundreds of millions of dollars in US aid.

He also said he would ask Congress to provide $200 million in budget support for Jordan this year as it cares for more than 450,000 Syrian refugees.

"This will mean more humanitarian assistance and basic services, including education for Syrian children so far from home, whose lives have been upended," he said.

At least 120,000 Syrian refugees are in the sprawling northern border camp of Zaatari alone, and Jordan has repeatedly complained that the growing numbers of Syrians, expected to reach 700,000 this year, are draining its resources.

Obama also warned during his visit that the use of chemical weapons by Syria's armed forces would be a game changer that would invite international action.

He wrapped up his first visit to Israel as president on Friday by giving Prime Minister Benjamin Netanyahu, with whom he had feuded in his first term, a hug.

He also pulled off an unexpected coup, engineering a deal to restore diplomatic relations between estranged US allies Israel and Turkey, concluded in a tarmac telephone call at Tel Aviv airport before he departed for Jordan.

Netanyahu apologised to Turkey and his counterpart Recep Tayyip Erdogan for a deadly raid on a Gaza aid flotilla and announced a full resumption of diplomatic ties as well as compensation to end a near three-year row.

Obama cautioned that the deal, though important, should not spark too much euphoria, saying: "You know, this is a work in progress. It's just beginning."

"There are obviously going to still be some significant disagreements between Turkey and Israel not just on the Palestinian question but on a range of different issues."

The centrepiece of Obama's visit to Israel was a powerful direct appeal to young Israelis on Thursday when he declared the two-state peace solution was very much alive and their only hope of true security, urging them to try to see the situation through Palestinian eyes.

He also accepted that Israel had a right to ensure its self-defence, but urged time for his diplomatic push to work to halt Iran's controversial nuclear programme.

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