Earlier this month, the president said he favored taking control of Gaza and displacing the Palestinian population of the devastated seaside enclave. But Egypt and Jordan flatly rejected cooperating.

For decades, American officials described the rulers of Egypt and Jordan as linchpins of regional stability. They made peace with Israel (in 1979 and 1994, respectively). They mostly avoided wars, coups and revolutions.

JERASH, Jordan — Izzaat Al-Hindi trudged down a passageway of the Jerash Refugee Camp, navigating potholes, garbage piles and drab, dilapidated buildings. He still remembers the day his family fled here from Gaza, almost 57 years ago.