Obama told reporters Jordan is among the United States' best friends and partners in the world, and pointed out "the fact that they are in such a difficult neighborhood makes the relationship between our two countries that much more important."
Obama praised Abdullah for encouraging "peace and prosperity" in the region.
Obama said the two leaders spent a "great deal of time" in their meeting going over "key subjects," including the importance of continuing to consult closely to encourage the Palestinians and Israelis to resume direct talks aimed at arriving at a two-state peace solution.
"We talked about the importance of us continuing to consult closely together to encourage the Palestinians and the Israelis to come back to the table and negotiate in a serious fashion a peaceful way forward," Obama said. "And the Jordanians have taken great leadership on this issue, and we very much appreciate their direction on this issue."
Abdullah said the outcome of the Israeli-Palestinian talks remains unclear.
"Although this is still in the early stages we have to keep our fingers crossed and hope that we can bring the Israelis and Palestinians out of the impasse," the king said.
The president ignored a question shouted aloud about efforts by the Quartet -- the United States, Russia, United Nations and the European Union -- to help shape a peace agreement between the Israelis and Palestinians.
Iran, Iraq and Syria also were on the leaders' talking points agenda.
Obama gave the king high grades for being the first leader to call for Syrian President Bashar Assad to step down in the face of ongoing deadly government violence against Syria's people.
"I want to thank him for his willingness to stand up," Obama said. "Unfortunately, we're continuing to see unacceptable levels of violence inside that country."
Obama said the United States will "continue to consult very closely with Jordan to create the kind of international pressure and environment that encourages the current Syrian regime to step aside so a more democratic process can take place inside of Syria."
Obama complimented the Jordanian leader for "guiding political reform inside of Jordan."
"I think his majesty has been ahead of the curve in trying to respond to the legitimate concerns and aspirations, both politically and economically, of the Jordanian population," he said.
The king also was to meet with members of Congress and various political and economic officials.
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