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The coup that ousted Mr. Morsi was “was a major blow to Hamas, the Palestinian branch of the Muslim Brotherhood,” said Mr. Phillips. “Egypt’s army has cracked down on arms smuggling across the border, which has weakened Hamas.”

But whether this crackdown will affect Hamas remains uncertain. “I doubt that Hamas has been weakened enough to abandon its ideological commitment to destroying Israel and replacing it with an Islamist state,” Mr. Phillips said.

Others suggested that the security and political crises inside Egypt are likely to stand in the way of any serious cooperation between Washington and Cairo with regard to Hamas.

“I think it’s far to early to put pressure on the Egyptian military to try to deal with Hamas,” Mr. Cordesman said.

“There are too many other issues that divide Egypt,” he said, going further to note the lack of progress elsewhere on the Israeli-Palestinian front. “There’s no clear peace process yet to show that negotiations are serious.”