Meeting a longstanding Turkish demand, Netanyahu apologized for the deaths of nine activists aboard the Turkish ship and promised to pay compensation to their families, according to a statement from his office.
The Israeli and Turkish leaders agreed to restore normal relations, including the return of ambassadors and cancellation of Turkish legal proceedings in absentia against Israeli troops involved in the raid, the statement said.
Concerned about the deterioriating situation in Syria, the Obama administration had been been anxious to mend relations between Turkey and Israel, two major regional powers on Syria's borders.
"The United States deeply values our close partnerships with both Turkey and Israel, and we attach great importance to the restoration of positive relations between them in order to advance regional peace and security," Obama, who joined the phone conversation, said in a statement later.
"I am hopeful that today's exchange between the two leaders will enable them to engage in deeper cooperation on this and a range of other challenges and opportunities," the statement added.
In eliciting the Israeli apology, Obama sought to bring together two estranged regional powers that he has worked for years to reunite. It came as Obama was preparing to fly to Jordan on the last leg of his Middle East trip. Erdogan has been among Israel's sharpest critics in recent years, largely over Israel's policy in the Gaza Strip.
Speaking in Amman, Jordan, later in a joint news conference with King Abdullah II, Obama said there would "still be disagreements" between Israel and Turkey. "But they also have a whole range of shared interests, and they both happen to be extraordinarily strong partners and friends of ours. And so it's in the interest of the United States that they begin this process of getting their relationship back in order, and I'm very glad to see that it's happening."
In the call, U.S. officials said, Netanyahu acknowledged Israeli "operational mistakes" during the raid on a ship bound from Turkey for the strip, part of a six-vessel convoy trying to deliver humanitarian aid to the enclave in defiance of an Israeli blockade.
Obama had asked Netanyahu to issue such an apology to Erdogan, an Islamist politician, since the May 2010 incident, when Israeli commandos seeking to block the Mavi Marmara from reaching Gaza killed eight Turkish citizens and one American of dual nationality on board.
In 2010 and 2011, John F. Kerry, then a senator from Massachusetts and now secretary of state, sought reconciliation between Netanyahu and Erdogan, but the Israeli leader resisted issuing an apology. On his first trip as secretary of state in February, Kerry urged Erdogan personally to tone down anti-Semitic rhetoric and rebuild ties with Israel. He even scolded the Turkish leader publicly about a particularly incendiary comment.
Netanyahu finally relented on the last day of Obama's first presidential visit to Israel, apologizing in the phone call with Erdogan.
In a statement later, Erdogan's office said he "accepted this apology" on behalf of the Turkish people. It said the two also "agreed to work together to improve the humanitarian situation in the Palestinian territories."
But the aid group that organized the flotilla promptly rejected the Israeli overture.
Huseyin Oruc, vice president of the group known in Turkey as the IHH Humanitarian Relief Foundation, said the apology and compensation for family members of those killed were not enough.
"Israel has killed nine friends of mine," he said. "We need to find these killers and punish them in a proper way." He called for the commandos who killed the activists on the Mavi Marmara to be sentenced to life in prison.
Oruc also said Israel should pay compensation to those injured in the incident and to IHH for damage to the Mavi Marmara. And he said he wants Israel to remove IHH from its list of terrorist organizations. Then, he said, it would be "no problem" for IHH to cooperate with the Israeli government to deliver aid to Gaza in the future.
Asked whether the apology represented a victory for Obama, Oruc replied: "If there was a victor, it was the participants of the flotilla."
Turkey, a NATO member, had been a rare Muslim-majority nation with a traditionally strong relationship with Israel. But the Israeli operation against the Mavi Marmara caused a major breach in their important economic and cultural relationship.
The Israeli government, which left Gaza in 2005 but still controls its air space, coastal waters and cargo crossings, had said its soldiers opened fire in self-defense after boarding the ship and coming under attack.
Senior administration officials traveling with Obama said that during his meetings with Netanyahu this week, the president discussed the importance of making the call to Erdogan.
The phone call took place in a trailer on the grounds of Ben Gurion International Airport, the administration officials said, and the Turkish and Israeli leaders spoke for about half an hour. At one point, the officials said, Obama joined the call.
One of the senior administration officials briefing reporters later aboard Air Force One said the apology and conversation mark a "first step" toward normalization of relations between Israel and Turkey.
In a statement, the Israeli government said Netanyahu "expressed regret over the deterioration in bilateral relations and noted his commitment to working out the disagreements in order to advance peace and regional stability."
Netanyahu "made it clear that the tragic results regarding the Mavi Marmara were unintentional and that Israel expresses regret over injuries and loss of life," the statement added. "In light of the Israeli investigation into the incident, which pointed out several operational errors, Prime Minister Netanyahu apologized to the Turkish people for any errors that could have led to loss of life and agreed to complete the agreement on compensation."
Obama's diplomatic intervention came just before he concluded a three-day visit to Israel and the occupied West Bank, where he met with Palestinian leaders.
He arrived soon afterward in Jordan, where a military band greeted him on his arrival at the royal compound of King Abdullah II. It is Obama's first official visit to an Arab nation since he delivered his address to the Muslim world in June 2009 from Cairo.
The visit to Jordan is largely a show of support within the country for Abdullah, an ally who is confronting a mounting humanitarian crisis with a deluge of Syrian refugees, mounting calls inside his country for faster political reform, and increasing frustration over the lack of a peace process in a country whose majority is of Palestinian descent.
The two were slated to hold meetings, then appear Friday evening at a joint news conference.
But before leaving Israel, where Obama enjoyed a warm reception from a public skeptical of his first-term intentions, he honored a pair of historic figures whose lives traced the arc of the Zionist movement: Theodor Herzl, its chief theoretician who never lived to see the Jewish state he envisioned, and Yitzhak Rabin, the prime minister who died trying to secure that state through a fateful peace effort with the Palestinians.
In a visit weighted with symbolism, Obama made his way on a clear spring morning to Mount Herzl, where, with Prime Minister Benjamin Netanyahu and President Shimon Peres by his side, he stepped toward the granite tomb, marked simply "Herzl" in Hebrew.
The visit, which other foreign leaders have avoided, was meant to underscore Obama's understanding that the modern state of Israel traces its roots to the Bible, not to the Holocaust. That history, in the minds of many Israelis, gives the state a greater claim against Arab opposition to the land that comprises their modern state.
An Austrian journalist, Herzl identified rising anti-Semitism in late 19th-century Europe and conceived the Zionist movement — a project to create a Jewish, democratic state in Palestine. He died in 1903 and was reburied on Mount Herzl the year after the state of Israel's creation in 1948.
As is Jewish custom, Obama then laid a stone on Herzl's tomb, a sign of respect and a visible sign of a visit to someone who has died.
Then Obama walked to Rabin's grave, where he also laid a stone that administration officials said was taken from the grounds of the Martin Luther King Jr. Memorial in Washington.
Rabin fought for Israel's independence in 1948, and as a prime minister signed the 1993 Oslo accords with Yasser Arafat, then chairman of the Palestine Liberation Organization.
In addition to formally recognizing Israel and the PLO, the agreements set out a path toward the creation of a Palestinian state in the West Bank and the Gaza Strip. The accords also created the Palestinian Authority, giving Palestinians limited self-rule for the first time since the 1967 Arab-Israeli war.
Rabin and Arafat, along with Peres, the foreign minister at the time, shared the Nobel Peace Prize in 1994.
The following year, Rabin was assassinated by a Jewish extremist opposed to the accords, and Rabin's grave has been a common stop for U.S. presidents ever since. Obama declined to visit Arafat's tomb during a Thursday visit to Ramallah, another customary gesture for many visiting dignitaries.
Near Rabin's grave site on Friday, six members of the late Israeli prime minister's family — including a daughter, a son, a granddaughter and a grandson — stood beneath an evergreen awaiting Obama.
"A remarkable man," Obama said as he shook hands with Dalya Rabin-Pellosof, Rabin's daughter.
The group chatted before Obama stepped to the grave, set down his stone and adjusted a wreath placed there by two American military personnel.
After visiting the Hall of Children at Yad Vashem, the hilltop Holocaust memorial near the Mount Herzl cemetery, Obama said, "For here we see the depravity to which man can sink, the barbarism that unfolds when we begin to see our fellow human beings as somehow less than us, less worthy of dignity and of life."
"And yet, here, alongside man's capacity for evil, we also are reminded of man's capacity for good — the rescuers, the Righteous Among the Nations who refused to be bystanders," he added. "And in their noble acts of courage, we see how this place, this accounting of horror, is, in the end, a source of hope."
Obama then set off to visit the Church of the Nativity in Bethlehem, just south of Jerusalem in the occupied West Bank. The church is built on the purported birthplace of Jesus.
A sandstorm grounded Obama's planned helicopter ride to Bethlehem, forcing him to drive the route that took him past a 24-foot high cement barrier that Israel built to separate Israelis and Palestinians a few years ago.
The barrier, designed to cut down Palestinian suicide bombings at the time, runs deeply into the West Bank at certain points along its more than 400-mile route. Israeli officials say it could someday serve as the state's de facto border, although many Palestinians view the barrier as a symbol of Israel's enduring military occupation of the West Bank and East Jerusalem.
Scattered street crowds were on hand as Obama's motorcade entered Palestinian territory. One group of storekeepers waved and blew kisses at the motorcade.
But there were also a couple of large protest signs. "No return, no peace," one said, apparently referring to the issue of refugees. "Gringo, return to your country," said another.
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