The meeting between the leaders of the two Arab countries that have signed peace treaties with Israel came after US President Donald Trump's administration suggested it would not insist on a Palestinian state for a Middle East peace agreement.
"The two sides discussed ways to push the stagnant Middle East peace process, especially in light of US President Donald Trump's administration coming to power," a presidency statement said.
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A two-state solution "with a Palestinian state... with east Jerusalem as its capital is a nationalist principle that cannot be conceded".
After meeting Israeli Prime Minister Benjamin Netanyahu in Washington earlier this month, Trump said he would entertain a "two-state and a one-state" solution.
But his ambassador to the United Nations, Nikki Haley, later tempered this stance, saying Washington "absolutely" supports a two-state solution but wants new ideas on how to move forward.
The two-state solution -- a Palestinian one alongside Israel -- has long been the cornerstone of US and international policy, and the seeming American shift was greeted with hostility from other world powers.