Barack Obama, the US president, has pledged an additional $200m in humanitarian aid this year to Jordan to help with Syrian refugees after the two leaders met for talks in Amman.
Jordan's king and the country's top military brass welcomed President Obama on Friday as the leaders headed into talks focusing on the conflict in Syria.
More than 400,000 refugees have crossed into Jordan to escape two years of bloodshed at home, crowding refugee camps and overwhelming aid agencies run by this important US ally in the Middle East.
King Abdullah II says Jordan has "historically opened our arms to many of our neighbours ... that is a challenge we just cannot turn our backs on."
"Refugees will continue to come ... but the problem is the burden it is having on Jordan - $550m per year."
Obama emphasised US support for Syria by saying, "We have led with deeds, we are the single-largest humanitarian donor to the Syrian people."
The US president acknowledged the problems of adding military support to Syria: "The US often finds that if it goes in militarily it is criticised; if it does not, people will ask why not?"
On Syrian President Assad's legitimacy, Obama was clear: "[Assad] has lost all legitimacy because he is willing to slaughter his own people."
"I am confident that Assad will go - it is not a question of if but when ... so we have to think about what comes after that."
Middle East tour
Obama also will seek to bolster Jordan's efforts to reform its government in an attempt to stave off an Arab Spring-style revolution that has led to the downfall of longtime leaders in Egypt, Tunisia and Libya.
On Saturday, Obama planned several hours of sightseeing, a tour of the fabled ancient city of Petra before the return trip to the White House.
Before arriving in Jordan, Obama closed a three-day visit to Israel, another important US ally in the region, by paying respects to the nation's heroes and to victims of the Holocaust.
The Israeli President Shimon Peres and Prime Minister Benyamin Netanyahu were present at Tel Aviv's Ben Gurion airport on Friday to see off the US president.
During the trip to Israel the US president reaffirmed US commitment to Israel.
He also expressed support for a two state solution where Israel and Palestine can co-exist as sovereign states.
At the Church of the Nativity, Obama ducked to enter through its small Door of Humility. Manger Square, the plaza in front of the church, was almost deserted except for security personnel.
"Gringo, return to your country," read a sign held by a small group of Palestinian protesters who watched the presidential motorcade roll into Bethlehem from Jerusalem after it passed through Israel's controversial barrier in the occupied West Bank.
Earlier, Obama visited Israel's most powerful national symbols, paying homage at the Holocaust memorial and the graves of Theodor Herzl, the founder of modern Zionism.
He also visited the grave of Yitzhak Rabin, the Israeli prime minister, assassinated in 1995 by an extremist Jew over peace moves with the Palestinians.