President Barack Obama arrived in refugee-flooded Jordan on Friday after scoring a diplomatic coup just before leaving Israel when Prime Minister Benjamin Netanyahu apologized to Turkey for a 2010 commando raid that killed nine activists on a Turkish vessel in a Gaza-bound flotilla.

The apology, long sought by Turkish Prime Minister Recep Erdogan, eased strained feelings between Turkey and Israel, two vital U.S. allies in the Middle East.

It happened in a phone call to Erdogan during a final meeting between Obama and Netanyahu at Ben Gurion International Airport in Tel Aviv minutes before Air Force One departed for Jordan to complete the president's Middle East swing. It is the first foreign trip of his second term.

A statement from Netanyahu's office said the apology included an offer of compensation. However, there was confusion later when the Israeli government dropped a reference in its original statement to normalized relations between the countries with a return of ambassadors.

There also was no word on whether the once-close nations would resume the joint military exercises that were suspended after the flotilla raid.

Turkey had been prosecuting four Israeli soldiers in absentia and Israel initially said the two leaders agreed to the cancellation of legal steps against the troops. Later, however, its amended statement omitted that action as well.

Regardless of such confusion, Obama hailed the development as an important step forward for both countries.

"For the last two years, I've spoken to both Prime Minister Netanyahu and Prime Minister Erdogan about why this rupture has to be mended," he told a news conference after talks with Jordan's King Abdullah II. "During my visit (to Israel), it appeared that the timing was good for that conversation to take place."

At the airport earlier Friday, Obama said, he and Netanyahu "agreed that the moment was right" to place the call to Erdogan and "they were able to begin the process of rebuilding normal relations between the two countries."

Obama arrives in Jordan on last leg of trip

The later stop in Jordan focused on the civil war in neighboring Syria, with Abdullah telling reporters that the conflict has caused 460,000 refugees to flood his country and more were on the way.

That equals 10% of Jordan's population, and the total could double by the end of the year, the king said in asking for more help from the international community as his country also deals with internal reforms in response to economic woes that are raising public dissatisfaction.

Obama said he was working with Congress to provide an additional $200 million to Jordan this year to help deal with the refugee influx, but he remained steadfast in his refusal to pledge U.S. military assistance to the Syrian opposition movement, as called for by critics at home and abroad.

"The United States often finds itself in a situation where, if it goes in militarily, then it's criticized for going in militarily, and if it doesn't go in militarily, then people say, 'why aren't you doing something militarily?'" he noted, arguing that a multilateral approach would yield more effective and accepted results.

At the same time, Obama repeated past warnings that his stance on military involvement could change if the Syrian government uses chemical weapons.

In Israel, the last-minute diplomacy added a flourish to Obama's first visit to the Jewish state as president.

While the two nations have a key strategic partnership, with the United States supplying military aid and diplomatic support as Israel's most vital ally, Obama and Netanyahu had famously frosty relations during the president's first term.

With both beginning new terms after Obama's re-election last year and Netanyahu's recent formation of a new government, the president's visit was an opportunity to reset the relationship and signal unified positions on major issues such as the Middle East peace process and Iran's efforts to develop a nuclear weapon.

Obama and Netanyahu met several times during the president's three days in Israel, which also included a state dinner where Israeli President Shimon Peres awarded him the country's highest civilian honor.

Before leaving Israel, Obama paid tribute to the father of modern Zionism in a symbolic visit to Theodor Herzl's grave.

Joined by Peres, Netanyahu and U.S. Secretary of State John Kerry, Obama also visited the grave of former Prime Minister Yitzhak Rabin, who was assassinated in 1995.

Both stops were intended to bolster Obama's standing with Israelis by demonstrating his understanding of the history of the Jewish state.

Obama placed a stone at each grave from the grounds of the Martin Luther King Jr. memorial in Washington in a gesture to link the African-American struggle for freedom with the struggle by the Israeli people for a homeland.

The president also visited the Holocaust memorial Yad Vashem, where he turned up the "eternal flame" of remembrance of the millions of Jewish victims of Nazi death camps in World War II.

Obama called for the world to follow the example of nations that intervened in Nazi genocide.