“Sisi is worse than Netanyahu, and the Egyptians are conspiring against us more than the Jews,” said Salhan al-Hirish, a storekeeper in the northern Gaza town of Beit Lahiya. “They finished the Brotherhood in Egypt, and now they are going after Hamas.”

Egypt and other Arab states, especially the Persian Gulf monarchies of Saudi Arabia and the United Arab Emirates, are finding themselves allied with Israel in a common opposition to Iran, a rival regional power that has a history of funding and arming Hamas.

For Washington, the shift poses new obstacles to its efforts to end the fighting. Although Egyptian intelligence agencies continue to talk with Hamas, as they did under former President Hosni Mubarak and Mr. Morsi, Cairo’s new animosity toward the group has called into question the effectiveness of that channel, especially after the response to Egypt’s first proposal.

As a result, Secretary of State John Kerry turned to the more Islamist-friendly states of Qatar and Turkey as alternative mediators — two states that grew in regional stature with the rising tide of political Islam after the Arab Spring, and that have suffered a degree of isolation as that tide has ebbed.

But that move has put Mr. Kerry in the incongruous position of appearing to some analysts as less hostile to Hamas — and thus less supportive of Israel — than Egypt or its Arab allies.

For Israeli hawks, the change in the Arab states has been relatively liberating.

“The reading here is that, aside from Hamas and Qatar, most of the Arab governments are either indifferent or willing to follow the leadership of Egypt,” said Martin Kramer, president of Shalem College in Jerusalem and an American-Israeli scholar of Islamist and Arab politics. “No one in the Arab world is going to the Americans and telling them, ‘Stop it now,’ ” as Saudi Arabia did, for example, in response to earlier Israeli crackdowns on the Palestinians, he said. “That gives the Israelis leeway.”

With the resurgence of the anti-Islamist, military-backed government in Cairo, Mr. Kramer said, the new Egyptian government and allies like Saudi Arabia appear to believe that “the Palestinian people are to bear the suffering in order to defeat Hamas, because Hamas cannot be allowed to triumph and cannot be allowed to emerge as the most powerful Palestinian player.”